Selective Service Modernization Act of 2020 This bill makes changes related to the Selective Service System and induction into the U.S. Armed Forces. The bill requires the expungement of an individual's criminal conviction, other than for a crime of violence, upon the individual's induction into the U.S. Armed Forces. The bill also requires that the records of Selective Service registrants are periodically updated to exclude persons no longer subject to induction into the U.S. Armed Forces (e.g., deceased persons and persons receiving Social Security Disability Insurance benefits).