In my case the cats used the trays were I was germinating seed as a cat liter box

About all you could do is make the area unappealing to them. Perhaps layering the roof with something like chicken wire, which cats hate to walk on, would work. You can't draw the wire too smooth and taut otherwise it won't be effective - it needs to have some depth and texture to it that makes walking, sitting, sleeping uncomfortable.

Having worked at a various nurseries including a large growing operation that had some 25 greenhouses, I know how important cats are in these situations to control vermin :-) We only had one cat that 'belonged' to the nursery and she spent evenings out and about doing her job and the days sleeping in the office. But I'm sure an assortment of her friends from neighboring properties visited and helped with the rodent populations. They never appeared on top of any of the houses, however, perhaps because they were too tall, the roof pitch too steep and with no ready access. But I was never there in the middle of the night so who knows!

I had a cat who would use the shade cloth as a means of climbing up, then he'd walk around or perch at the apex. he liked the view and used it as an aide for hunting. he scared the bejeesus out of the other cats when he'd slide down the sloped side and pounce. he was very annoyed the time he took a flying leap to climb up, only to slide back down because there was no shade cloth to grip onto. perhaps a means of foiling their initial jump up the GH would prevent them from getting up. Or a spray of water whenever they are up there, to encourage them to find a warmer, drier spot. (I wouldn't spray them too meanly, or they'll do more damage trying to scamper away).

Hoo boy - I so know this problem. I had to use the hose, and I also put up tape where they were climbing.

My barn cat did this for years until he got too fat and old to climb them. Yeah, he used the shade cloth for the climb. I never found any damage to the poly from it, so just let him at it. He has, however, been shut up in each of the greenhouses on occasion accidentally at night. Each house has a cat-sized exit hole in the end wall.

The most obnoxious thing he does is laying in seedling flats in winter or early spring. They get so warm and toasty in the sun. Not much I could do to stop him from that and he still does it. Too sunny and hot to dome them.

Mine never used the germination trays as litter pans, but he tried that in my heated sand-based propagation frames. I ended up covering them with plastic trays when not in use. Can you blame him on a cold day? LOL.