There may be alternatives, but this worked like a charm.
I just cut up an old (but clean) t-shirt, and it worked perfectly.
I recommend working in an area about 6" x 6" until it is complete, and then move on. Apply plenty of Scratch Doctor, and you'll want to press and scrub firmly until the scuff marks loosen up and start to disappear.
Clean off the area with a dry cloth to remove any remaining Scratch Doctor. As you can see it makes a big difference.