The pet in your care is covered by The Pawshake Guarantee. This covers medical emergencies and veterinary care for the pet while they are in your care. As the sitter you are also covered in case of third party claims. For more details of The Pawshake Guarantee, please refer to this page:
Unfortunately, we do not cover loss, theft or property damage under our Guarantee.
If a pet damaged your belongings or property, you have to reach a direct agreement with the owner based on what happened. It's possible that yours or theirs insurance will cover for it.