Protecting Seniors Access to Health Care Act This bill modifies funding and eligibility for various benefits and programs, including several established under COVID-19 relief laws. With respect to funding, the bill provides supplemental funding for the Public Health and Social Services Emergency Fund to reimburse certain health care providers for expenses or lost revenue attributed to COVID-19; and rescinds certain unobligated funds that were provided to the Department of the Treasury for payments to state, tribal, and territorial governments to mitigate fiscal impacts of COVID-19. The bill also applies certain modified payment limits to certain rural health clinics that enrolled in, or applied to enroll in, Medicare in calendar year 2020. Furthermore, the bill prohibits individuals who were unlawfully present in the United States on March, 11, 2021, from receiving premium subsidies in the event they lose employer-sponsored health insurance due to involuntary termination or a reduction in hours, or direct payments provided to certain taxpayers to mitigate financial hardship during the COVID-19 emergency. The bill also prohibits individuals who were incarcerated on that date from receiving the direct payments.