Now that it is shot, little. You can increase contrast a bit. There is a Dehaze tool, I never used it but I would guess it looses resolution like a sharpening tool. I think that there is a mucho complex method that would involve shooting a plain image of the screen only and then digitally say using Ps subtract that image "data" from the cat image. But this is lightyears over my head.

I do know how you might have avoided the problem partly to begin with. Manually focus on only the cats face with a very shallow depth of field, say f/ 2.8 to 4.5, depending on how "fast" your lens is, but certainly not at f/8 or f/22. You might even want to focus slightly beyond the cat's eyes, say on the ears and still keep the eyes sharp. No AF though, that will get confused by the screen. If the cat were far enough from the screen the screen would disappear. Outdoors that can be done similarly but at greater distances with a telephoto lens to shoot right thru a chain link fence. Say like this:

A professional wildlife photographer I know showed me and the rest of her class this. You can shoot right the the fence and it disappears from the image. I've done it also at a large cat sanctuary for photographing a Tiger thru bars. We were both too close so the bars still show as a blur and softened the entire image a bit.