Safer Neighborhoods Gun Buyback Act of 2021 This bill authorizes the Department of Justice's Bureau of Justice Assistance (BJA) to make grants to states, local governments, or gun dealers to conduct gun buyback programs. The BJA may distribute smart prepaid cards for use by a state, local government, or gun dealer to compensate individuals who dispose of firearms. Additionally, the bill establishes a new criminal offense for using or accepting a smart prepaid card in the acquisition or transfer of a firearm or ammunition. A violator is subject to a fine, up to two years in prison, or both.