Inclusion Criteria:
* Histologically confirmed HCC, that is unresectable, recurrent, and/or metastatic.
* GPC3-positive tumor expression confirmed by immunohistochemistry (IHC).
* For the dose-escalation cohort: ≥10-20% tumor cells, ≥2+ IHC.
* Beginning with the RP2D confirmatory cohort: ≥ 50% tumor cells, 2+/3+ IHC.
* Must have received at least first-line systemic therapy for HCC and have experienced disease progression on, or intolerance to, that therapy.
* Life expectancy of at least 4 months per the Investigator's opinion.
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1.
* Measurable disease by RECIST v1.1.
* Child-Pugh score of A6 or better.
* Adequate organ function.
Exclusion Criteria:
* Pre-existing illness (e.g., symptomatic congestive heart failure) that would limit compliance with study requirements.
* Active, uncontrolled systemic bacterial, fungal, or viral infection. Subjects with Human Immunodeficiency Virus (HIV), hepatitis B, or hepatitis C are eligible provided their infection is being treated and the viral load is controlled.
* History of malignancy other than HCC within 5 years before screening, except adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other malignancies with low risk of recurrence.
* Known brain metastases or other active central nervous system (CNS) involvement, including leptomeningeal disease. Subjects with brain metastases that have been adequately treated (no evident neurological deficit and no steroid or anti-epileptic therapy for brain metastases) are eligible.
* Pregnant or lactating women.
* Currently receiving or ending (\< 14 days from date of consent) liver tumor-directed therapy (e.g., radiation, ablation, embolization), or hepatic surgery.
* Concurrently receiving other investigational agents, biological, chemical, or radiation therapies, while participating in the study.
* Active autoimmune disease requiring systemic immunosuppressive therapy.
* Presence of portal vein tumor thrombus (PVTT) classified as grade Vp4, or any invasion into the inferior vena cava (IVC), except for subjects with IVC invasion who have been treated and radiographically stable for at least 6 months prior to screening.
* Ascites requiring active treatment, such as a requirement for paracentesis or escalation of diuretic doses. Exception: Subjects maintained on a stable dose of diuretics with controlled, asymptomatic ascites are eligible.
* Active gastrointestinal (GI) bleeding event ≥ Grade 3 per National Cancer Institute (NCI) Common Terminology for Adverse Events (CTCAE), version 5.0, within 6 months prior to screening.
* Coagulation abnormality defined as international normalized ratio (INR) \> 1.7, unless the elevation is due to therapeutic anticoagulation that, in the Investigator's judgment, can be safely managed in the context of study procedures.
* History of organ transplant.
* HCC involving greater than 50% of the liver volume.
* Experienced allergies to any component of the study drug (ECT204), mouse immunoglobulin, or iron-dextran, or have a history of severe hypersensitivity, including anaphylaxis.
* Previously received other gene therapy (e.g., chimeric antigen receptor T-cell \[CAR-T\] therapy); exception: prior oncolytic virus therapy is permitted.).
* Contraindication for undergoing leukapheresis procedure or receipt of conditioning agents
