Hello American_Deer,
Check out Apple's recommendations for how to clean you AirPods:
How to clean your AirPods, AirPods Pro, AirPods Max, and EarPods - Apple Support
If you can't clean off your AirPods' case, you can order a replacement (if you have AppleCare+, you might be able to receive a new case free of charge depending on the circumstances).
Note that buildup can occur on your AirPods from frequent use and dust, etc. If this is a problem other than these stated conditions, the limited warranty that came with your AirPods may cover the damage.
I hope this helps. Have a nice day.