The non-profit's lawyer, Peter D. Russin, filed notice in Tampa bankruptcy court that he also wants to question her parents George and Cindy Anthony under oath.
Anthony told Orange County detectives in the summer of 2008 that her 2-year-old daughter was kidnapped by a baby sitter and was missing.
TES organized several multiday searches in the fall of that year that attracted volunteers from across Florida, who came to Central Florida to help look for the missing toddler.
But during Anthony's 2011 murder trial, defense attorney Jose Baez said Caylee drowned in her family's swimming pool and there was no kidnapping.
TES sued Anthony, claiming it wants to be reimbursed for $110,000 spent on the searches.
"Our client, we truly believe, was damaged purposely by fraud," Russin said.
Anthony, who has been in hiding since being acquitted of murder in Caylee's death, filed for bankruptcy in Tampa early this year. She claimed she owes roughly $800,000, and the bulk of that debt is to Baez.
She listed TES as one of her creditors, with an unknown amount of claim.
In May, TES filed a complaint in bankruptcy court objecting to Anthony's attempt to discharge her debts through bankruptcy. Russin filed three deposition notices this week.
He wants to depose Anthony on July 22 in St. Petersburg — the region where she is supposedly living now. Russin's filing requests Anthony produce a list of documents ranging from her communications made to law-enforcement and comments made to the media.
Russin wants to depose both George and Cindy Anthony on July 23 in Orlando, and has asked for similar documents.
"We're just trying to get the truth," Russin said.
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