Telehealth Modernization Act of 2024 This bill modifies requirements relating to coverage of telehealth services under Medicare. Specifically, the bill permanently extends certain flexibilities that were initially authorized during the public health emergency relating to COVID-19. Among other things, the bill allows (1) rural health clinics and federally qualified health centers to serve as the distant site (i.e., the location of the health care practitioner); (2) the home of a beneficiary to serve as the originating site (i.e., the location of the beneficiary) for all services (rather than for only certain services); and (3) all types of practitioners to furnish telehealth services, as determined by the Centers for Medicare & Medicaid Services.