What to do if you accidentally damaged your ceramic floor tiles:
If your floor tiles' glossy, glazed surface appears to have worn out, there is really nothing you can do to restore the finish as glaze needs to be fired or baked onto the ceramic. If you know where to find similar tiles, you can ask your contractor to hack out and replace the damaged section. But this might cost you more to do a small section as it's a specialist job, but worth it if your bathroom is fairly new.
Or consider integrating new tiles with contrasting designs, just like in the bathroom pictured, instead of trying to match the existing one for a change!
If you don't fancy doing an expensive renovation, just get a big rug and simply cover up the splotchy tiles.