..., on a marble-like surface? The counter top looks like marble, but a friend told me it's fake marble. It has a cigarette burn on the right side about 1" across.

use a light sandpaper to scrub off the burnt colour!! then polish it!! it should do!!!

Start with a 120 grit sandpapercontinue with a 220 grit overlapping what you did.follow with a 400 then a 800 always making the circle bigger and bigger as you go up in sandpaper grits.Finish with a car compound and wax. This should be done all over the counter to get an even finish. The two car compounds are essential so get the professional one.