First, they must check to see if their warrantless arrest was for a misdemeanor offense, or if they were arrested for a felony with the charge later reduced to a misdemeanor upon review by the prosecutor. Subsection (b) of Penal Code Sec. 17.033 permits a $10,000 bond after a warrantless arrest for a felony.
But even if we assume it was a misdemeanor arrest, the person is not going to recover the fee. The proper remedy would have been to petition the court to reduce the bond, or for a refund of the excessive portion of a bond actually posted with the court. As the fee was paid to a third party, the bail bonding company, and the court was apparently never asked to revisit the issue, the fee becomes a matter of contract between the defendant and the bail bonding company as opposed to something that will involve or concern the court.

