Screening Partnership Reform Act of 2020 This bill revises the Screening Partnership Program of the Transportation Security Administration (TSA) to authorize the operator of an airport to select a qualified private screening company with which the operator prefers the TSA enter into a contract for screening services at that airport; direct the TSA to enter into a contract with a private screening company only if the cost of providing screening services at the airport is equal to or less than the cost to the federal government of providing the same screening services, and entering into the contract would not compromise aviation security or the effectiveness of the screening of passengers or property at the airport; allow a private screening company to use screening supervisors who have been trained and certified at a Federal Law Enforcement Training Center to administer comparable on-site training and certification to private security screeners at an airport that is participating in the screening partnership program; and require a private screening company in the program to annually submit recommendations to the TSA on new approaches to screening processes and procedures that would enhance the screening of passengers and property at the airport.