More muscle than just soap and water is required. A scotchbrite scrubbie with some soft scrub cleanser should do the trick. If it is actual quartz or a corian type material, it shouldn't really be stained, but there are probably surface bits of dirt that have become discolored and are adhering strongly.

Try a little bit of Dawn dish detergent, wipe it over the area and let it sit for while before washing off. Good luck

Smooth cooktop cleaner such as Cerama Bryte and a soft cloth. On the rare occasions when something marks my quartz counters this takes it right out.