Well... hmmm....
I've had a dog in the past that LOVED to swim, and frankly was quite hard to keep him out of water... (he thought just the hose was an amazing miracle and would do the JRT broing broing broing at the water biting it), it would have been harder than keeping the other JRT away from her tennis balls, LOL.
It's probably a lot of fun for them if they have kids.
I'm thinking... maybe some pre-screening material would help? Like window screen or some wire mesh or something?
With an issue that was never expressly forbid... I would try to find an amicable way to deal with it. Maybe simply ask them to check the filter themselves when the dog has been in the pool?
As I doubt it was in the lease, "no dogs in pool", and probably not in the pool sign-age (?), I don't think you have any immediate legal recourse... however, if it actually does do damage (despite your normally scheduled cleanings being documented), when the renters move out you could deduct the replacement or repair from the deposit?
I'd be a little careful of the issue with your dad and them. I'm sure if he is doing what he was contracted to do, all will be fine.... but if you ever end up in court for some reason, and it comes out that your father was acting as your agent and crossed the boundary lines of the tenant/landlord relationship (like entering a house without due notice) you could get in trouble.
Not saying that's happening.... but it just came to mind, as we were in a position once, as tenants with a landlord whos boyfriend would not stop using her key to enter our home illegally. As long as the tenants are in residence, they have rights to privacy.