If a prisoner is ordered by a court to make monthly payments for the purpose of paying the balance of filing fees or costs under section 2963 of the revised judicature act of 1961, Act No. 236 of the Public Acts of 1961, being section 600.2963 of the Michigan Compiled Laws, the department shall remove those amounts from the institutional account of the prisoner subject to the order and, when an amount equal to the balance of the filing fees or costs due is removed, remit that amount as directed in the order.