On receipt of a request from the legislative body of a county, city, or other political subdivision or agency of the State, to which a legislative grant of tide and submerged lands has been or may be made, or at its own instigation, the commission may survey, monument, plat, and record in the office of the recorder in the county or counties in which such lands are located, the area of state lands described in such act of the Legislature. Whenever such survey and plat has been made at the request of a grantee of the State, the costs thereof shall be repaid by such grantee to the commission.