Illegitimate Court Counteraction Act of 2023 This bill imposes sanctions against International Criminal Court (ICC) employees and associates if the ICC investigates or pursues charges against certain individuals. The bill defines certain classes of individuals as protected individuals, including (1) members of the U.S. Armed Forces, (2) employees and contractors of the U.S. government who assist the U.S. Armed Forces, and (3) certain members of the armed forces of U.S. allies or partners. If the ICC investigates or pursues charges against a protected individual, the President must impose visa- and property-blocking sanctions against those foreign persons (individuals or entities) that, as ICC employees or associates, aided in the investigation, arrest, detention, or prosecution of a protected individual. Additionally, if the ICC investigates or pursues charges against protected individuals, the President must impose visa-blocking sanctions against any foreign individual who is (1) an employee of the ICC; (2) acting as an agent of the ICC; or (3) an immediate family member of those aiding the investigation, arrest, detention or prosecution of a protected individual. The property-blocking sanctions do not apply to the importation of goods. The visa-blocking sanctions do not apply to admissions to (1) further important U.S. law enforcement objectives; or (2) comply with international obligations, such as the United Nations Headquarters Agreement.