Is this something that comes from the inside?
If so, this is probably because of the nature of the plastic material....
over-time, like most plastics, they will discolor when exposed to light.... and the move controller has a light inside so the light may yellow over use as well from the glass.... unless its an LED light.
you're probably going to have to open up that controller and see if you can clean it from the inside...
if its smoke causing the damage you really can't clean it. Its chemically bonded with the soft material. if its yellowed, the damage has already been done
For general cleaning you want to use hot water and a clean rag every so often as a preventative measure. Its a soft rubber and susceptible to the cleaning agents cleaning products so try to stay away from them as much as possible and if you DO use them make sure to rise the surface thoroughly to get any remaining cleaner off.
Warm water is all you need.