I doubt you'll be able to get it off. Any kind of abrasive action with a stiff brush will take the surface paint off the tile. You could try high pressure air through a blow gun hooked to a compressor, but I don't think it will help. Replacing the tile is the best option. If it's been there a while, it has probably discolored/faded somewhat and new tile (if you can find the same) will stand out. If possible, take tiles from a small adjacent room (closet/bath) and use them to replace the sooty tiles. Replace all of the tile in the small room so it matches and doesn't draw attention. You'll have a few more replacements too. Be sure to store them flat....
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