Try "Barkeeper's Friend" clenser and a white nylon scrubbing pad. The clenser should be in your supermarket, right next to the Comet and Ajax. It's very good at removing "minor" metal abrasions, and usually won't affect the tile's finish. After this, I would try using the clenser with a pumice stone (also in the cleaning aisle under the name "Pummie"). This is rougher than the white nylon and will probably scar a highly glossed tile, though a matte finish tile should still be okay. Aluminum is a soft metal and so it's unlikely tha the tiles themselves have been scarred by the shutters. But if you can "feel" the marks with your fingernail, you may have to plan on replacing the tiles afterall.
Remember to "test" these scrubbing recommendations in some inconspicuous area before unleashing them on your floor. The tile under the refridgerator is usually a good spot for testing and it often needs cleaning anyway. Give it a really agressive scrub, wipe it clean, and then use a flashlight or other bright light to check the reflective quality of the finish on the tile. If it looks "dull', your glaze is too soft for that particular remedy.
Best of luck,