Hi Anne, unfortunately once you scratch glass there's really no way to remove them. However, if you have streaks or stains that appear to be scratches you can clean them away. Here's what I have done: https://www.exquisitelyunremarkable.com/2017/04/the-best-way-to-clean-glass-stove-top.html
You can also peek at this post: https://homeguides.sfgate.com/fix-scratched-glass-cooktop-27383.html
Hi Anne: check these sites:
To clean it, as long as the dirt is superficial, there is no problem cleaning a vitroceramic hob, but as soon as there are splashes of grease, sugar, tomato, sauce, it's more difficult to clean.
This homemade recipe will help you clean your vitroceramic hob, it will be like new.
You will need: baking soda, dish washing liquid and vinegar and allso a bath towel as big as the vitroceramic hob.
Start by pouring the vinegar into a spray bottle and sprinkle the entire surface of the hob.
Sprinkle baking soda on the hob.
In the sink or bucket, pour hot water and dish soap. Wear gloves and immerse the towel in very hot water.
Twist it, but not completely dry, and spread it on the ceramic hob. Wait 15-20 minutes before removing the towel.
With a soft brush, rub the surface of the hob, then wipe it. Normally, all the dirt is already gone with this method. If your hob is really dirty, you may have to start again.
Finally, spray white vinegar on the vitroceramic hob and wipe it with a microfiber cloth: the plate will be completely clean!
The Cerama Bright does really work to help remove the burnt on stuff on a glass cook top and Whirlpool makes one as well as a Cook top Protector. I use separate Micro Fiber cloths for each product, different colors help with keeping them straight.
HOWEVER.... you can keep the heavy cleaning to a minimum by making sure that the cook top is clean BEFORE you start cooking. Dust and other stuff (like salt or spices) settles on the cook top and a quick going over with Windex and paper towels can prevent stuff from burning on when the element heats.
NEVER use a soapy dish cloth... it leaves a residue that bakes on as soon as the top heats up...making a "base" for other stuff to attach to. If you do use a soapy cloth.... rinse with a clean cloth... and then finish up with a cleaning using a good window cleaner like Windex and Paper Towels
My husband was VERY bad for spraying pans with Cooking Spray while they were sitting on the stove top... leaving a greasy ring that immediately cooked on the glass top.... I finally cured him of this by making him use the Cooktop Cleaner and Protector (first scraping all the burnt stuff with the razor blade)... now he sprays over the sink and uses the Windex before cooking his eggs