There is special glass top stove cleaner. It's a cream. Look around in her cleaning supplies, as I bet she has some.

Also, a paste of baking soda and small amount of water left on the spot often helps (see the box).

Maybe you hadn't noticed the panel area before and it's always been there.

This is probably fixable. Don't get too upset.

I've. Had success using Barkeepers Freind powser getting burnt oil off porcelain. Make a paste- spread, let sit for 15-20 clean off. Gently-repeat a few times. May work.

Be very careful with anything abrasive ... you don't want to make it worse.

Barkeepers is not abrasive- it is an oxy cleaner

Oxalic acid. It dulled (very fine scratches) the surface of my quartz countertop.