So I then messaged the person to send the horse back and I accepted another. I made sure this time to hit the Move to Stable button and it took me right back to the contract page again saying the deed was completed and horse returned to sender. To make sure before I said something, I accepted a different person's horse and I put the cursor over the Move to Stable button and (where it shows what address the button leads to) it had the reclaim contract link.
Just wanted to let Nef know in case it hadn't yet been caught
