Looks like they are getting damaged. Could be from other fish or parasites causing an irritation that they try to resolve by rubbing up against the coral. I would recommend Tetracycline, but if you're moving, it may not be worth the bother.

Thanks for the tip. I really like these guys, but I can't imagine who would want them looking like that. I'd love to find them a good home!! Christy

Perhaps a local petshop would take them in?

Oh, I hadn't considered that. Though, I'm not sure the Petsmart or Petco will take them, and the good store is about 30 minutes away. I may call and ask them. Thanks :) Christy

A more "mom & pop" petshop would tend to be more accommodating.

No, this looks like ulcers, a fungal problem. My gouramis got it. I have found that Gouramis are very hard to keep. Everyone told me that when I got my tank, but I wanted to prove them wrong. I didn't. Do a web search for fungus infections in aquarium fish/gouramis and see what you find. Good luck.

Yes, if you google "ulcers on gourami", you will get many sites, some with pictures, and you will see that this is what it is. I'm sorry... been there done that. A pet store will not want to put these fish in with their stock.