Medically Tailored Home-Delivered Meals Demonstration Pilot Act of 2021 This bill requires the Centers for Medicare & Medicaid Services to establish a demonstration program to allow hospitals to provide medically tailored, home-delivered meals to Medicare beneficiaries who have a diet-impacted disease (e.g., kidney disease) and have daily living limitations. Participating hospitals must (1) retain a physician, registered dietitian or nutrition professional, or clinical social worker to screen, monitor, and coordinate services for individuals who receive meals through the program; and (2) contract with experienced organizations for meal delivery. Hospitals may choose to also provide meals to an individual's primary caregiver or to a dependent under the age of 18 who resides in the same household.