Telehealth Modernization Act This bill modifies requirements relating to coverage of telehealth services under Medicare. Specifically, the bill extends certain flexibilities that were initially authorized during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019). 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.