What do you do if owner doesn't want dog back?

So my first day as a sitter on Rover and I got a beautiful st Bernard puppy for the night. She is so sweet. The owner said she was house trained but that couldn't be further from the truth. Despite bathroom breaks every 30 min she still peed everywhere. She also doesn't know anything. We taught her to sit. I contacted the owner to coordinate drop off of her puppy. It turns out they aren't sure they want her back. They offered to pay us additional days and keep her until they can figure things out. Not sure what we should do. Our heart breaks for this dog but we can't keep her. Should I try and get the owner to surrender the dog to us and then find a rescue that will take her? I don't believe the dog is in any real danger or neglect, but the fact that this is our first time on Rover as a sitter and we get someone who wants to get rid of their dog makes me think they have tried this before...don't know if they even have records or papers for the dog. Any advice? My husband wants to give the dog back and move on - it's not our problem. I feel for the dog!