Pay Our Border Patrol and Customs Agents Act This bill provides FY2024 appropriations for the salaries and expenses of certain U.S. Customs and Border Protection (CBP) employees who are required to work during a lapse in appropriations (i.e., government shutdown) in FY2024. Specifically, the bill provides appropriations to CBP for the salaries and expenses of agents of the U.S. Border Patrol and officers of the Office of Field Operations who are excepted from furlough (i.e., required to work) during a lapse in discretionary appropriations in FY2024.