Make a cardboard cutout of the MDF shape and go to your local suppliers, see if you can find a like for like replacement. If you find an exact match and you have the skills and tools for the job then replace the trim. Don't do this if you don't know how, it could go wrong and leave you with worse problems!
If you cannot find a like for like replacement you'll need to patch it up with wood filler. First sand, then do a rough patch-up of the worst area, using the template you made to keep it roughly to shape. Let it cure, then do a fine patch using the template again to keep it all to shape. Sand, then paint.
Cats like MDF because their claws sink in, it's a problem. Next time get a sisal rope cat tree or two and place them strategically to catch their attention as it's always easier to get them to stop if they have something else to go for. Keep their claws trimmed as well. The first time you trim them the cat will complain a lot, but if you do it every couple of weeks they get used to it.
