I'd suggest that you make a paste with baking soda and water. Put it on the areas and let it sit for a while so that it can work. Then wipe/rinse off. If the stain persists, repeat until it's gone. Wishing you the best.
Hot soapy Dawn water and a sponge scrubby.
I agree with Kelli. Dawn is neutral and not likely to damage stone. If you have quartzite, that is natural stone. Quartz composite, however, such as silestone is tough as nails. I still would use dawn.
I'd try Dawn, maybe baking soda paste, but there's a product called Cerama Bryte Granite & Quartz Cleaner and Polish that I've had good luck with. Check their website to see if it's safe for your brand of quartz.