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I clean my screen less than once per month so that isn't what I meant - simply that if I feel actual debris on the tip or screen (which is very rare) I clean that particular debris - not that I scrub the screen.
This issue can occur with light palm/finger prints. Test it. Lighting brush screen with microfiber - remove all fingerprints. Then open new note and draw lines too to bottom and side to side. Next place hand on screen a few times (more than normal to accelerate for testing) and then draw lines too to bottom and side to side on new note. Feel the areas of different response.
 
Microfiber and a minuscule amount of warm water goes a long way cleaning your iPad display. Every once in a while, I may use Whoosh, but my display is cleaned regularly, so it's rare I use anything else.
 
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