Matt and Melanie Capobianco filed the petition in their home state of South Carolina Sept. 9, while the biological father of "Baby Veronica," Dusten Brown, was still appealing court orders to hand over the girl in Oklahoma, the Tulsa World reported Monday.
The Capobiancos asked the Oklahoma court to make Brown and the Cherokee Nation, Brown's tribe, reimburse them for attorney's fees and other expenses, the newspaper said. The girl, 4, was handed over to the Capobiancos last week.
No dollar figure for the compensation was given.
2014: The Year in Music [PHOTOS]