Thats what all my gadgets look like when I don't think and spray air scents at my ceiling fan, before I hide them under a pillow or in a drawer. I don't know what kind of spray, but it's definitely residue left by a spray.
A damp microfiber cloth or less than damp magic eraser might get the job done.
Avoid chemical surface cleaners and paper towels. And I'll even say avoid rubbing alcohol. Its good for cleaning woulds and a few copper contacts, but its shitty for cleaning transparent plastic.
If you must use a cleansing solution, google plastic-safe ones. If you use a Magic Eraser, then use light strokes and let the foam do the work. A magic eraser is basically just a soft foam pad thats micro porous. Thats why it can get things up like permanent market, because what it's actually doing is chipping away at dried marker on a micro level