A Study to Evaluate C-CAR031 in Glypican-3 (GPC3)+ Advanced/Recurrent Hepatocellular Carcinoma (HCC)

Inclusion Criteria: 1. The participant voluntarily participates in the study, and the individual or their legal guardian signs the informed consent form (ICF). 2. 18 \~ 75 years of age at the time of signing ICF. 3. Clinical trial participants with advanced HCC confirmed by histopathological or cytological examination with the following requirements (no mixed HCC-cholangiocarcinoma permitted): * Barcelona Clinic Liver Cancer (BCLC) stage C or B (not amenable to surgery/local treatment, includes ablative therapy, interventional and radiation therapy) or stage II-III ( not amenable to surgery/local treatment, includes ablative therapy, interventional and radiation therapy) per China liver cancer staging (CNLC). * Child-Pugh score ≤ 6. * Participants must have a GPC3-positive tumor as determined by a central laboratory using an analytically validated IHC assay. Participants with unknown GPC3 status are not eligible for this study. 4. Participants who have progressed or are intolerant to at least two prior lines of standardized systemic therapy, and lack of other effective treatments; Systemic therapy intolerance is defined as: drug-related adverse reactions or side effects caused by systemic therapy (including but not limited to targeted therapy, immunotherapy) in patients with HCC that prevent patients from continuing treatment. 5. At least one measurable target lesion (as defined by RECIST v1.1) that has not undergone prior local therapies such as radiotherapy (excluding lesions with radiologically confirmed progression after local therapy), and has not been utilized for research pre-screening biopsies (if only one target lesion exists and must undergo tissue biopsy, baseline tumor imaging must be performed at least 14 days after the biopsy). 6. ECOG performance status score of 0 or 1. 7. Minimal life expectancy ≥12 weeks, per the Investigator's discretion. 8. The left ventricular ejection fraction (LVEF) measured by echocardiography ≥45% and reported as non-impaired. Measure must be within 28 days prior to apheresis. 9. The laboratory testing results meet the following study requirements. Blood routine examination * \*Absolute Neutrophil Count (ANC) ≥1.0×10\^9/L. * Absolute Lymphocyte count ≥ 0.3×10\^9/L. * \*Platelet count ≥ 75×10\^9/L. * Hemoglobin ≥ 80g/L. \* With no transfusion or blood component transfusion received within 28 days prior to blood sampling or within 14 days prior to apheresis; or, with no granulocyte colony-stimulating factor (G-CSF) or other hematopoietic stimulators administered as supportive treatment within 28 days prior to blood sampling or within 21 days prior to apheresis. Blood biochemistry * Serum total bilirubin ≤ 2.5×ULN (upper limit of normal) in the absence of Gilbert's syndrome, or ≤ 3×ULN if the patient has Gilbert's syndrome. * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤5×ULN. * Albumin ≥ 2.8 g/dL. * \*Calculated creatinine clearance ≥30ml/min. ＊As determined by Cockcroft-Gault equation using actual body weight. Coagulation • Prothrombin time International normalized ratio (PT-INR) ≤1.6. 10. Participants with Hepatitis B virus (HBV) infection or history of infection (as characterized by positive HBsAg, \[hepatitis B surface antigen\], and/or detectable HBV DNA, and/or HbcAb \[hepatitis B core antibody\]) are eligible for inclusion only if: * The participant is treated with antiviral therapy, as per institutional practice, to ensure adequate viral suppression (HBV DNA less than 2,000 IU/mL or 10,000 copies/mL). * Participants who test positive for HBsAg and/or HBcAb must initiate standard antiviral therapy according to the most recent edition of the Guidelines for the Prevention and Treatment of Chronic Hepatitis B at least 1 week prior to cell infusion, with tenofovir recommended as the preferred antiviral agent. 11. Female participants of childbearing potential must test negative for pregnancy in serum or urine; non-sterilized participants (males and females) agree to take effective contraceptive measures for at least 12 months or CAR-T below lower limit of detection (LLD) by droplet digital polymerase chain reaction (ddPCR) whichever occurs first after C-CAR031 infusion (including participants who have only received lymphodepleting chemotherapy). Exclusion Criteria: 1. Known life-threatening allergies, hypersensitivity, or intolerance to the CAR-T product or its excipients, including dimethyl sulfoxide (DMSO). 2. Known allergies to lymphodepleting agents, including fludarabine and/or cyclophosphamide. 3. History of hepatic encephalopathy within past 6 months prior to apheresis or requirement for medications to prevent or control encephalopathy (eg, lactulose, rifaximin, etc infused for purposes of hepatic encephalopathy). 4. Participants with central nerve system (CNS) diseases such as epilepsy, severe cerebral vascular stenosis, or those who have had a cerebral infarction or other cerebral vascular accidents within 6 months, or other diseases with obvious neurological symptoms (including mental illnesses). 5. Uncontrolled or intercurrent cardiac or pulmonary diseases, including but not limited to, chronic obstructive pulmonary disease with obvious symptoms, and moderate or above persistent asthma, with a known history of non-infectious pneumonia requiring steroid treatment, or those presenting with acute exacerbation or progressive non-infectious pneumonia at baseline, unstable angina, severe arrhythmia, severe non-ischemic cardiomyopathy history or myocardial infarction or cardiac vascular surgery treatment occurred within 6 months. 6. History of organ transplant including liver. 7. Prior treatment with: * Any CAR-T therapy. OR * Any therapy that is targeting GPC3. 8. The tumor volume is larger than 50% of the liver tissue. 9. Main portal vein cancer embolus (Vp4, cancer embolus in the main trunk of the portal vein, with or without blood flow) on pre-LDC imaging. 10. History of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolism (venous port or catheter thrombosis or superficial venous thrombosis are not considered "significant") during the 3 months prior to apheresis. 11. Clinically meaningful ascites, defined as any ascites requiring non-pharmacologic intervention (eg, paracentesis) to maintain symptomatic control, within 6 months prior to apheresis. Participants on stable doses of diuretics for ascites for ≥ 2 months prior to apheresis are eligible. 12. Uncontrolled pleural effusion or pericardial effusion requiring recurrent drainage procedures (once monthly or more frequently). 13. Cancer-related spinal cord compression, leptomeningeal disease, or brain metastases unless asymptomatic, treated, and stable radiologically (defined as 2 brain images, \[both after treatment\], should both be obtained at least 4 weeks apart and show no evidence of intracranial progression) and resolved or stable clinically; not requiring continuous corticosteroids at a dose above10 mg/day prednisone or equivalent for at least 4 weeks prior to apheresis. 14. Received radiation therapy within 6 weeks of apheresis, or received local radioactive particle implantation within 6 months or 3 half-lives (whichever is longer). 15. Received local treatment (such as: surgery, ablation, transarterial-chemoembolization \[TACE\]) within 4 weeks of apheresis, or existence of unhealed wound. 16. Received inactivated or live attenuated vaccine within 4 weeks prior to apheresis. 17. Blood transfusions within 14 days and/or growth factor support within 21 days prior to apheresis. 18. Received systemic treatment and did not meet the minimum requirement for washout before apheresis: * Immune checkpoint inhibitor: within 5 half-lives or 2 weeks (whichever is shorter). * Chemotherapy, small molecule targeted therapy: within 5 half-lives or 2 weeks (whichever is shorter). * Experimental anticancer drugs or other anti-cancer systemic treatment including Chinese herbal medicine, Chinese patent drug: within 5 half-lives or 2 weeks (whichever is shorter). * Systemic dosing of steroid(s) (excluding: intranasal, inhaled, topical steroids or local steroid injections \[eg, intra-articular injection\]; systemic corticosteroids at physiologic doses not exceed 10mg/day of prednisone or its equivalent; steroids as premedication for hypersensitivity reaction \[eg, computed tomography \[CT\] scan premedication\]) or other immunomodulators (eg. Interleukins, interferons, thymosins, etc.): within 5 half-lives or 2 weeks (whichever is shorter). 19. Has a history of other primary cancers, with exceptions of: * Tumors with low metastatic potential that have been cured by excision (such as: basal cell carcinoma of the skin). * Cured carcinoma in situ. 20. History of or with active immunodeficiency diseases (including but not limited to HIV \[Human immunodeficiency virus; positive HIV 1/2 antibodies\], systemic lupus erythematosus, inflammatory bowel disease, rheumatoid arthritis, myasthenia gravis, Graves disease, pituitary inflammation, multiple sclerosis, neuromyelitis optica spectrum disorders, Guillain-Barré syndrome, and chronic inflammatory demyelinating polyradiculoneuropathy, etc.; The following are exceptions: participants with vitiligo or alopecia, participants with hypothyroidism who have stabilized after hormone replacement therapy, any chronic skin disease that does not require systemic treatment, and other diseases that deemed not clinically significant per the Investigator's discretion). 21. Active Hepatitis C virus infection (Hepatitis C virus \[HCV\] antibody positive and HCV RNA positive). 22. According to the medical history, the participants who were known to have co-infection with HBV and hepatitis D virus (HDV). 23. Syphilis infection (Syphilis antigen and antibody positive). 24. Active infection requires systemic treatment (prophylactic administration of anti-infection medication is permitted; those who initiated antiviral therapy for HBV infection before screening must continue treatment throughout the study; for HBsAg-positive and/or HBcAb-positive participants not on antivirals before screening, antiviral therapy must be initiated at least 1 week prior to cell infusion, with tenofovir preferred as the antiviral agent). 25. History of cardiac arrhythmia (such as multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia), which is symptomatic or requires treatment (NCI CTCAE (National Cancer Institute Common Terminology Criteria for Adverse Events) v5.0 Grade 3); unless controlled by pacemaker (discussion with the Study Physician required); symptomatic or uncontrolled atrial fibrillation despite treatment, or asymptomatic sustained ventricular tachycardia. 26. Clear clinical evidence of dementia or changes in mental state. 27. Heart failure: heart function of Class III or IV per the New York Heart Association (NYHA) heart function classification standards. 28. Participants use full-dose long acting oral or parenteral anticoagulants or thrombolytic agents for therapeutic (as opposed to prophylactic) purpose. Use of short acting direct oral anticoagulants for therapeutic and prophylactic purposes are permitted. 29. Participants with any of the following hemorrhage-related conditions: Active bleeding events ≥ Grade 3 (per NCI CTCAE v5.0) within 12 months prior to apheresis, Documented history of gastrointestinal variceal bleeding, or clinically significant history of upper gastrointestinal hemorrhage. 30. Obvious risk or tendency of bleeding. 31. Being in pregnancy or lactation period, or having plan to conceive during the study period. 32. History or current evidence of any condition, therapy, or laboratory abnormality that, per the Investigator's discretion, might confound the results of the study, interfere with the participant's safety and/or study compliance. 33. Major surgery within 2 weeks prior to apheresis, or has surgery planned during the study, or within a minimum of 4 weeks after study treatment administration. (Note: participants with planned surgical procedures to be conducted under local anaesthesia may participate). 34. Any unresolved toxicity NCI CTCAE ≥ Grade 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values. Participants with irreversible toxicity not reasonably expected to be exacerbated by treatment with study intervention including Grade 2 neuropathy maybe included after consultation with the Sponsor. 35. Patients with alcohol or drug abuse. 36. Participants with HLTV infection (HLTV antibody positive).