I try to make it very clear at all meet-and-greets that it's important for clients to disclose ALL bad habits or unusual behaviors so that I can be well prepared. I want us both to be confident that I'm the right sitter for the job and nobody runs into any negative surprises.
Since I started phrasing it that way, I've managed to avoid mishaps, but a good sign they're not being honest is glancing around the home for any signs of damage during the meet-and-greet. For example, I recently had a repeat client who insisted her dog was now fully house trained in the new apartment, but who (like yours) later said that some behavior I brought up was common (ripping up trash bags, chewing up treat bags, ripping pillows, etc.) despite not warning me at all. Had I visited her new place before accepting the booking, I would have seen broken blinds, chewed up windowsills, scratched up doors, etc.
You could potentially discuss adding a charge (usually I set it up as if it's a new booking) but that assumes the owner will be responsible and compensate you for the damage. If this is something you plan on doing part-time longterm, I recommend drafting up a contract for clients to sign. It might be worth investing in a short consultation with a lawyer (here I found one who did this for like $25 for 30 minutes). Clients who know they'll be expected to replace anything their animal damages are much less likely to omit details about bad behavior.
I'm sorry you're dealing with that, though. It's frustrating to deal with owners who don't respect your home or peace of mind.