I think a touch-up paint is your best bet. See if some local store sells formica repair kits. Probably a buyer will update the counter anyway. You could lay out some hand towels, but I'd want to be sure to disclose this anyway, after the good impression has been made.

Get an inexpensive stock laminate counter from a home center and replace the counter - you will need to pay a plumber to reinstall the sink. You could also get a sink / counter combo from a home center and replace with that - it depends on the length of the counter. You can get stock laminate for less than $100 and depending on the length, less than $50. The burnt counter is the sort of thing which really should be fixed before trying to sell a home. A cover up won't work and will just makes people wonder what else you are hiding while a new counter might help update the room a bit.

https://www.menards.com/main/c-3629.htm?Spec_ShopbyProductType_facet=Countertop