Well . . . .Upon taking a break from finishing Gatsby . . . .It is the immigration courts set up through the executive branch under the AG, so technically yes, but they operate as courts, hear evidence, appeals, bond hearings and issue orders (asylum, etc)
It seems to me that the federal district court has no jurisdiction or authority in the Garcia case at all. All Garcia decisions and orders must go through the DOJ’s immigration court system.
The immigration court has plenary authority over the Garcia claims and appeals from that court go to the Board of Immigration Appeals. Appeals from the Board go to the circuit court of appeals.
LibGuides: Immigration Law Clinic Research Guide: Immigration Courts and Appellate Review
LibGuides: Immigration Law Clinic Research Guide: Immigration Courts and Appellate Review

A federal district court might have habeas authority over somebody in Garcia’s position, but that is questionable since he was in a civil removal process and not criminally incarcerated.