Good tenants are worth their weight in gold, as are good landlords.
There are plenty of cats who don't damage anything or wee where they shouldn't. Let's hope, if they actually have got a pet living there, it's one of those.
If they have got a pet or moved in with an existing one without permission, it is regrettable, of course. It wouldn't be a deal breaker for me though. I would do the inspection first, see what that throws up, and take it from there.
It sounds like your tenants have come to look on the house as their home, which is understandable. It could even be a good thing for you OP if it means they want to stay, you want to carry on letting out the house, and they are generally good tenants. It could be much, much worse than a small pet and a tv on the wall, believe me.
There's rarely such a thing as a perfect tenant, perfect landlord, perfect owner-occupier. It's all give and take in my experience.