DIY - how to fix closet doors?

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So, here's a partial view of the damage:

[Petrichor]

That looks like it's only varnish deep. In which case you could sand them down and revarnish but I can't see the point if the cats are just going to scratch them up again. Wouldn't the landlady object to them being painted? I think if it were me I'd just face losing some deposit at the end of the tenancy.

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If it was real wood I could sand it but I tried and it "slips", it is more like tough plywood. And we would still need to re-varnish.

The cats have lost interest in that area. It would be difficult to scratch it again. i just want it to look better in case anyone comes -a couple if friends have seen it and have gone OMG! heaven forbid that the landlady sees that, if she does, she's not a fan of the cats and we'll be on our fanny's on the street. We already had that soap opera last year, don't want to have it again.

[2Enigma]

For DIY, think about living without the cats and pay to have the doors replaced, new furniture, new kitchen cabinets and hire somebody to deep clean the cat smell. If you have them, like a mother-in-law, live with it or do the obvious.

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The cats are no problem. To be honest, they scratched the doors climbing to the top shelf to sleep there in winter. I have attached a lock there, they can't get in, so they do not have any more interest in the doors and hence, won't scratch them no mo. Cat smell? Only the litter box area, and because it is summer.

I would like to fix that and change the furniture and all, but as I have said, we are doomed for destruction by wreckball -sometime in the not so near future, thank Goodness-, and hence any investments are not considered vital according to my landlady. OTOH, I like to keep the place at least presentable, I hardly ever have company, but for my own sake, staring at that eyesore is depressing. I have already invested in light fixtures and new furniture and other stuff, I am considering painting the place slowly by myself and hence I feel the doors could be prettied up without much fuss.

If they could be sanded this whole discussion would be moot...