I doubt it is etched, but it is probably permanently stained. I'd Google and try a poultice or two, but I'm not optimistic with a stain that dark and a stone so porous.

How close is the stain to your sink please? If it's adjacent, perhaps a sink change could save you.

I'd go for an acetone and/or lacquer thinner poultice. Saturate, cover with saturated paper towel, cover the paper towel with Saran Wrap and tape the edges. Check it in a day or so. May have to repeat. You run the risk of lightening, but spreading the stain.

Thanks for your replies. Six days later and with a baking soda and water poultice treatment it appears that the mark is mostly gone if not all gone, and I’m hoping it will lighten/dry out within the next few days.This is just completely unpredictable. The stain is on an island without a sink so I’m just keeping my fingers crossed at this point.

Flick a heat gun or a Bernz-O-Matic over it please. Don't go crazy.

Latest and last update: the spot has dried and I’d say it’s completely gone from my quartzite! There might be a shadow of the stain but no one but me will ever know. Maybe because I got the baking soda poultice on it right away, not sure. Thanks again for your help and comments. I hope others will benefit from this thread. I feel like I dodged a bullet with that one and learned a big lesson about what gets left on my countertops.