Can I reject an applicants request to withdraw their withdrawal?

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Lol no this is not a riddle. I actually had an applicant that was going through the screening process with the HOA of my community request to withdraw the lease agreement. The applicant did not want to wait any longer for an approval for the HOA and decided they wanted to move on. After informing the applicant several times that they will lose their deposit they kept trying to tell me that I owed them their deposit. The very next day they sent me a request to withdraw their withdrawal. I really do not want this person in my home right now. Am I allowed to reject this last request, legally? I already listed my home for rent again and am receiving inquiries for rent now. I have all withdrawal request in writing.