Spray a lubricant onto a nylon scrub brush. You can find spray or aerosol lubricants at any hardware store. Look for one that you would use on a door hinge to stop it from squeaking. Also, do not spray the lubricant directly onto a tiled surface, as some lubricants may stain tile grout.
Scrub the rubber vigorously with the nylon brush. Keep scrubbing until the rubber loosens.
Wipe away the loosened pieces of rubber with a paper towel or clean cloth.
Clean the tile as you normally clean it, with soap and water, a warm water and vinegar solution or a commercial cleaning spray.