Ceramic hob haze

[JK0]

One of my rentals has quite an old hob, though it still works perfectly. I have got all the burnt residue off it with a Stanley blade, but I still have a white haze in one of the rings, which seems to be scratched into the glass.

So far, I have tried Viacal and Bar Keeper's Friend on this, scrubbing with a green nylon scourer, but they don't make much impression. Is there anything else to try, or is the haze permanent?

[nukecad]

Does the haze disappear if you put cooking oil or water on it?

If so then it's fine scratches, on an old hob probably simply scratched by pans on the most used ring.
We all have one ring we use most for just one pan.