The authority may issue, sell, and deliver bonds to refund all or any part of its outstanding bonds, including the payment of any redemption premium and interest accrued, under such terms, conditions, and details as determined by the board. Bonds issued by the authority may be refunded in the manner provided by any other applicable statute, including Chapter 1207, Government Code. Bonds, the provision for the payment of all interest and applicable premiums on which and the principal of which has been made through the irrevocable deposit of money with the comptroller in accordance with the provisions of such an applicable statute, shall no longer be charged against the issuing authority of the authority, and on the making of such provision such issuing authority shall, to the extent of the principal amount of such bonds, be restored.