The county clerk shall issue a confidential marriage license upon the request of a notary public approved by the county clerk to issue confidential marriage licenses pursuant to Chapter 2 (commencing with Section 530) and upon payment by the notary public of the fees specified in Sections 26840.1 and 26840.8 of the Government Code. The parties shall reimburse a notary public who issues a confidential marriage license for the amount of the fees.