If the Joint Legislative Budget Committee advises the board that the Legislature desires to reconsider any part of the omnibus claim appropriation withheld by the Controller, no further action shall be taken with respect to that part and the money appropriated therefor shall revert to funds from which they were appropriated, pending further legislative action. The board, however, shall institute proceedings as provided in Section 920.6 to compel payment of the remainder of the omnibus claim appropriation withheld by the Controller.