If one absolutely needed to clean a modern thin plastic screen, an ultrasonic bath is probably the only sure way to guarantee no cleaning artifacts. Considering how seldom most operators need to clean the screen, a new replacement screen is probably a reasonable choice if your old one is too scratched, grease-smeared, or damaged.
I have, in the distant past, tried cleaning the textured Fresnel surfaces of the old F/F2/F3 screens using a cotton Q-Tip and alcohol. The best I could ever achieve was changing the screen from horribly soiled to merely soiled.
I agree with Bjørn that a bit of dust or even scratches on the focusing surface can actually be helpful when fine focusing. Dust spots on the non-focusing surfaces of screen or prism are much more annoying to me, since they hover just slightly out of focus.