Was told dog is house trained and when I left the room he tore up a lot of stuff what do i tell the owner?

I'm not sure what exactly the owners said to you, but to me "house trained" means potty trained, but it doesn't tell me anything about other potential problem behaviors, like chewing or separation anxiety. Additionally, I fully expect to see some anxiety behaviors with a new dog I'm boarding, regardless of how they react to being left alone at home, because this is an entirely new experience for this dog. Chewing releases endorphins, which helps dogs calm themselves, so it's one of those go-to behaviors for a stressed out dog.

I seriously doubt the owners lied; if this was something he did at home they very likely would have mentioned it to you because most owners do care about how their dog behaves, especially if they display any behavior that could be potentially dangerous for them. If this dog had a chewing habit at home, you can bet the owners would want to make sure there was no way he could accidentally chew on something dangerous to him. You can certainly mention the behavior to the owners, just to let them know that he does have some anxiety about being left alone in a new environment so they can take that into consideration if they need to board him again. For his safety, he may need to be kennel trained prior to any more boarding, or he may need a travel sitter or someone who can supervise him at all times. I would not ask for compensation.

If I do not know a dog I do not give him free roam of my house when I am not there. If I have to step out of the house, he/she will be gated in a certain area. Remember, our top priority is the dogs safety, so the fact that he was able to roam around and perhaps get into something dangerous was not a good idea. I would mention the anxiety part to the owner as Laura has stated, but do not ask for compensation. You'll have to determine if this is a dog you want back. His behavior is not unusual. Think about it, he's in a new home with a stranger, his owners are gone and now you left him alone. All this equates to anxiety. I'm sure the owner knows he does not like to be left alone, that is why they hired you or maybe they don't, that's why you should mention it. Dogs act differently when they stay with a sitter so maybe they have no idea this is how he behaves.

Unfortunately, this may be one of those things you add to the lessons learned category. Never underestimate what a visiting canine guest may do when left alone. Although it sounds like he was behaving well based on your experience up until then, he may have become stressed when you then left him (and he's not at his home). You may choose to use it as a tax deduction. I'd suggest you do Not ask the owner for compensation. The owner probably would have a different perspective, so I doubt that you'd get what you're seeking and you'd probably receive a negative review too (which will negatively impact your ability to grow your business).
There have been at least a couple similar discussions in the sitter to sitter section about damages. Here are a couple links I saw. https://www.rover.com/community/quest... & https://www.rover.com/community/quest...

Being a sitter has risks, but I would expect people to still have common courtesy. Owners paid for their dogs care, but it does not mean their dogs can do whatever in the sitters house without them taking part of the responsibility. Dogs are like children, if their children damaged things in their baby sitters house. How would a decent person not offer to compensate in any way? Human cant reason with dogs does not mean we cant reason with their owners.

Unfortunately there's nothing you can do. I always expect the dogs to loose their mind, they are pissed their owner left them with a stranger! You can nicely mention it to the owners that the dog misbehaved while you went to the store when they ask you how their dog was. But don't expect any compensation- if they offer sure, but that's the risk we all take.