This may help:
Hi Mom, I sure hope this helps! http://www.howtocleanstuff.net/how-to-remove-minor-scratches-from-marble/
Try re-sealing it to fill in the scratches
If the scratches are deep use CA glue that you get in Hobby Lobby [Cyanoacrylate glue] or real Super Glue. Before you glue use a magic marker for color mixing. Over glue the scratch. Let dry completely then take a straight edge razor and using a 90 degree angle scrape off the excess.
I have had success using car compound, put it on, let it dry to a haze and buff off. I used an electric buffer, but a microfiber cloth should work well.
You realy cNt unless you get a professional to buff it out
If polishing and sealing hasn't resolved it, I would get it professionally done. Good luck and stay well!
I love marble, but I hate when stuff like this happens. I agree with the buffing.
Try a little WD-40 on a cloth and rub the area. It worked for my floor.