Shift Back to Society Act of 2021 This bill directs the Department of Education to establish a pilot program that awards matching grants to historically Black colleges and universities to provide educational programs for eligible offenders to facilitate reentry into the community. An eligible offender is a convicted criminal offender who has been released from incarceration for not longer than one year or who is scheduled to be released from incarceration within one year. The Government Accountability Office must report to Congress on the results of the pilot program.