this sounds like a job for the caamera guys.
yes treeks, because of the other liquids/residues in the actual cleener stuff.
streeks because a tiney skin paricle or dandruff of a weird spec out of the air landed.
the cloth/paper/T shirt is eather not been rinsed well enough and has resins or oils still in the fibre (chuckum in the washer a couple times, works on shammy), or its not lint free.
too actaulay clean depends on how mucky you've been, but, one wipe off chuck it or use a different spot.
the question of removing the coating? ffffff try a dremal! the coating should NOT come off, even if using windoleen..and yes even on a camera lens. if it did the coating will fall off in a few weeks on its own acourd.
there is one sinario you'll not like, plastic lens can go soft with the rong stuff on it.(or they go dull..)
you dont leave the cleaner stuff on it..or it smears about.
get a lens pen, clear debry/large mountains and dust n grime with a brush,(unused brush, or...spead the paint that cleaned out all over it!) or lint free bog paper or some posh stuff, then lens pen it. no need to go silly though..
next best is a desent micro pore cloath, but, be aware the bit you just used is now a greasy smear spot.
ehhhh washing up liquid n rinse but make sure it dries out quickly...or risk the dreaded fungus! (toilet paper..one wipe off..chuck it).
if you've been around candles burning, then hmmm tars about the same to clean off, patients, some windowleen to start, the clean that off then clean the lens narmaly, yu cant clean off mountains and exspect it go in one, wipe once n chuck for best results.
(shhhh theres some top secret stuff called 'spit'...enzaymes in that quite often remove a stuborn bit..wipe it off and chuck, the cloth/tissue not the lens!).
if you need any off the net just shout up..15 quid a tub, free p+p lol.
yeh i know ...debortuary lol.