Border Wall Reimbursement Act of 2021 This bill requires the federal government to reimburse a border state for amounts that state has expended on the construction of a border security wall in support of federal efforts. To receive reimbursement, a state must submit within 180 days of the bill's enactment an accounting of the expenses incurred by the state and its municipalities and the total sum of such expenses. Certain funds made available to assist states and local governments during the COVID-19 public health emergency may also be made available to reimburse border states under this bill.