Lawyers acting on behalf of the US state of Kentucky told a panel of federal judges on Thursday that Kim Davis from Rowan County should pay $225,000 (£171,000).
They are challenging a previous court ruling that the cost should be met by taxpayers. Her legal team had argued the elected court clerk had held a position of public office.
The case dates back to 2015 when same-sex marriage was legalised nationwide.
Davis - a devout Apostolic Christian - believed her name appearing on marriage licences would amount to an endorsement of gay marriage, and she refused all together to issue the licences.
She was ordered by a court to issue the licenses after being taken to court by couples represented by the American Civil Liberties Union.
Having refused to back down, she found to be in contempt of court and jailed for five days.
The case was eventually dismissed when state politicians passed a law removing the names of county clerks from marriage licences in the state.
Davis' legal team has argued she should not have to pay the legal fees because, technically, she did not lose the case.
It is unclear when the federal judges will reach a decision.
Davis is no longer a court clerk after she was not re-elected to the post.
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