Question on Return of Security Deposit

[Joshua D.]

Hey guys,

  We are located in PA. I have a question regarding the return of security deposits.  We had a tenant who took a tour 3 times of our rental, signed the lease, gave us the first months rent and the security deposit, and asked if they could have the keys a week early, to start moving in.

Okay.  So 3 days prior to moving in, they text us saying that they don't like the broken register covers, and that they want a door on the downstairs room. Okay, no problem. We add a door but can't fix the register covers, as they would need to be custom ordered and we rent as-is. The next day, October 1st, 1 day prior to the official start of their lease on November 1st, they inform us that they just really decided that they don't like the house and don't want to move in.  I told her thank you for letting us know, and refunded their first months rent (same amount as the security deposit.) I had her sign a lease termination notice on the 31st of October, and they gave us back the keys and never moved in.

SO. I'm going through my papers a few months later and run across her lease termination agreement signed and rental agreement and think, eh. I don't need these anymore, it's settled. And throw them away. Yeah, stupid I know. But I've learned.

I get an email literally a week later where the 1 tenant (there were 3 of them on the lease, originally) is saying that I have no right to withold their security deposit and she's going to take us to court and retrieve double the deposit plus attorneys costs if I don't return it. 

What would you do? I wrote back advising that I'd be filing to retrieve the month of lost rent I had due to her backing out 1 day prior to the lease beginning, and she had already taken possession of the house by taking the keys.......Do I have a leg to stand on here, without a signed lease or termination?? 

Thank you guys!!!