Terrorist Deportation Act of 2023 This bill establishes that non-U.S. nationals ( aliens under federal law) identified in the terrorist screening database, except for lawful permanent residents, shall be deportable and inadmissible into the United States. The Department of Homeland Security (DHS) may temporarily waive the inadmissibility of such an individual if it is in the national security interests of the United States. DHS shall grant such a waiver only with the unanimous concurrence of the Department of Justice, the Federal Bureau of Investigation, the Office of the Director of National Intelligence, and the Department of State. An individual identified in the terrorist screening database shall be ineligible for various immigration benefits, including asylum, withholding or cancellation of removal, voluntary departure, or adjustment of status. DHS shall determine on an expedited basis whether to remove an individual identified in the terrorist screening database, if the individual has not received a waiver and does not have lawful permanent residence status. The individual shall be entitled to various protections, including the right to be represented by counsel (at no cost to the government) and judicial review.