He's beautiful and very naughty!
I would be inclined to go to a card shop this afternoon and buy a lovely blank greetings card to send to the people whose house he got into.
You can write a note of sincere apology for the damage he has done and explain how he came to get into the house.
You could then add that you would like to contribute to the cost of the clearing up of what he has done.
If you give your mobile number, they can then ring you at their convenience when they are at the house. I don't know what they will say - the best solution might be for you to pay for a cleaner to spend an hour in the house later in the week.
If you pop it through their door this afternoon, you will be on the way to putting this upsetting time behind you.