Ouch!. Some folks develop strategies to try to avoid it, like always (always!) pulling the pan off the burner when done cooking. There are two kinds of induction users: those who have made the mistake you made and those who have not yet made that mistake.

Otherwise, can you tell if the cloudiness is on top of the glass or beneath it? The time I made the mistake, it was surface marring (basically some goo from the pan.) IIRC, it took me four applications of the polishing creme to get it off. (Sorry, I can't recall whether it was Weiman's or Ceramabryte that I used.) If the cloudiness is not superfficial, I've got no suggestions. :>(

I've gotten cloudiness too, but it came right off. I'm wondering if the cooktop cleaner is the problem? Like the iron cleaner that's petroleum based so cleaning looks good but gets icky when it gets hot. We just use Seventh Generation dishsoap and a light vegetable-fiber (non-scratching) scrubbie. It might be a different cloudiness altogether, but it couldn't hurt to use a grease cutter like Dawn and see if that's the problem.

Same happened to me today. It appears to be under the surface. There is nothing to clean off. So sad.

If underneath, it is possible for the unit to be disassembled and the under surface cleaned (except where there are controls, as those might be secured to the glass). However removal and disassembly is not recommended because it is a big project requiring disassembly directions, electro-mechanical skill, and necessary muscle.