TxBuilder said:
Scratches are likely there forever.
A copy:
Why does the ceramic glass surface of my range look worn?
There are several possible causes. Cleaning up spills promptly, regularly cleaning the entire cooktop with Cooktop Cleaning Creme and using only smooth-bottomed pans will help you keep your cooktop looking great with less effort.
If your cooktop has tiny scratches or abrasions, clean it with recommended cleaning agents (such as Cooktop Cleaning Creme). To prevent scratching, make sure you use only smooth-bottomed pans, and keep the bottom of the pans as clean as possible. Don't slide pans - either glass or metal - across the cooktop.
If your cooktop has metal marks, you can remove them with Cooktop Cleaning Creme. To avoid getting future marks, don't slide metal pans or utensils across the cooktop.
If you notice brown streaks and specks, these marks could be the result of spills that you didn't remove promptly or spills that you wiped with a soiled cloth or sponge. Soiled pan bottoms could be another cause of these marks.
If there are areas with a metallic sheen, they're caused by mineral deposits from evaporated water and food. You can remove them by cleaning with Cooktop Cleaning Creme.
If you notice pitting or flaking, it's probably the result of sugary boil-overs that weren't promptly removed.
jeff.