I would go to the manufacturer's website and see what they suggest. Or call them.

We had the same problem, and also with the through-the-door water dispenser. I made a 10% solution of bleach and warm water and sprayed it on the entire set-up. It worked, and did no damage to any surface or working part. I'll probably have to repeat this process in the future.

This has always happened to us with those things and we're on our third such refrigerator.

This is not to mention what is in the holding tank at the back of the fridge. Never knew this until we moved and the refrigerator we had then had the tank visible. It was plastic semi-transparent, and I could see all this sludge in the bottom of it. Yeah, and that's what we'd been drinking. Think about it -- water (especially city water) in a tank for year after year that never gets cleaned or even rinsed out. It's disgusting. That is when we decided not to reconnect the water line to the icemaker. We took the icemaker out of the freezer and now we have lots of extra room in there too!

Unfortunately when we got our new fridge, which we fell in love with, it came with an icemaker. But we've never used it or the water line. The other good thing about this decision is that we never have to worry about the water line breaking.

The manufacturer's website, or the original manual should have cleaning instructions.

But this is exactly why I will never have through-the-door ice or water dispensers. The last were a major PITA. Never again.