Like an idiot, I burnt my ceramic glass stove top

[Dozyproduction]

As the title says, I used my ceramic glass stove top to light the coals. Started doing this without looking to see if there'll be any future consequences and now the predictable white haze has showed up and is unwilling to leave. 

Do any of you have any experience with how to fix the situation? Was thinking using a car surface approach and do some fine grit wet sanding and buffing with polish. Of course that's for clear coat and this is for ceramic glass. 

Any help would be really appreciated. Thank you

[Jawmichael]

First