I only have light scratches from the bottom of my door, if you have deep scratches I would recommend ROCOL RTD
http://www.ebay.co.uk/itm/Rocol-Rtd..._Metalworking_Supplies_ET&hash=item56662655d7
you will also need a polishing wheel for best results
This might help
Dip a nonabrasive 180-grit pad into water to moisten. Sprinkle a tiny amount of abrasive cleaner onto the wet, nonabrasive pad. Wipe the nonabrasive pad over the surface of the scratch, rubbing gently with the grain of the stainless steel.
Continue to rub the pad over the scratched area, applying light pressure, until it blends in to the surrounding stainless steel or disappears completely. For slightly deeper scratches, switch to a pad with a little more grit, and keep rubbing with light pressure with the grain of the stainless steel.
Place a drop of stainless steel polishing solution onto a clean, soft lint free cloth. Rub the polishing solution over the surface, using small, circular motions. Continue to buff the area until no polishing solution remains on the cloth, and the surface area blends into the surrounding stainless steel.
Rinse the area free of abrasive cleaner, using clean water. Wipe the stainless steel dry with the lint-free cloth.
Repeat till your happy like I said 3 hours a side sorts mine