Knowing the Efficiency and Efficacy of Permanent Telehealth Options Act of 2020 or the KEEP Telehealth Options Act of 2020 This bill requires the Department of Health and Human Services (HHS) and the Government Accountability Office (GAO) to report on the availability and effects of expanded telehealth services under Medicare, Medicaid, and the Children's Health Insurance Program (CHIP) during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019). Among other information, HHS must detail its actions during the emergency to expand access to telehealth services and must analyze telehealth usage by certain demographic groups. The GAO must report on the efficiency and management of the telehealth expansion and related risks of fraudulent activity.