The standard advice would be to use a suede brush and suede cleaner.
But I hacked it with stuff I already had on hand..
You can dampen with water. You can dampen with vinegar. There are other solvents obviously.
I used vinegar. I also didn't use an actual suede brush. I used vinegar and three brushes.
Brush 1, for the toughest matting was a brass bristle brush like this:
Brush 2, a slightly stiff plastic bristle fingernail brush like this:
Brush 3, a similar fingernail brush with softer bristles for the finish.
Finish brushing in one direction only to get the appearance as consistent as possible with the nap all laying in the same direction.
Mine had sever matting on the ends and very black stains along one side. All of it came out. You mentioned "dents". There were some actual small dents like where the case might have been banged up against the sharp edge of a counter or something. Even those came out completely. Case looks darn good IMHO.
I have not seen your case but I bet you can make it look great. The evidence is how severe my case was and how nice it came out.
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Thanks, I have similar brushes on hand as I also do vintage felt hat repair. I'll give it a shot if it doesn't sell soon.