I'm not sure what's causing the grit but the safest thing to try would be baking soda and water. Make the baking soda into a paste then spread it stove top. Let it sit for several hours or even overnight. Wipe it off, spray with vinegar water then wipe that too. Rinse with plain water and it should come off. Wishing you the best.
What kind of stove do you have,...gas or electric? Glass top? Where is the grit from?
Try Cerama Bryte along with the correct scrubber for stove tops so that it does not scratch and it should come off. A container of Cerama Bryte should last you a full year, even if you use it every day.
It sounds like something burned on. Is it a glass or metal top? In general, soaking the charred area with a wet cloth will loosen it up enough to scrape it off. Bartender's Friend or a baking soda paste can help, too.