The BEST way to clean ceramic floor tile is with VINEGAR, the acid in it will take all dirt, grease and anything on top of the tile off with No GREASY feel afterwards.
Ceramic tile is pretty tough. You can use most anything. Be careful of abrasive cleaners like Comet,etc. The best thing is to start mild and work your way up. Yes,you can use a garden hose on it. Try...
Use white wine vinegar(medium amount) and some squeezed lemonjuice(fresh).
The vinegar will cut through any dirt,limescale or grime and the lemon will get rid of bad odours and smells.
Quite possibly wrong, but I'm wondering if automotive brake cleaner might work. The residue seems similar and many brake pads are ceramic.
Please try isopropyl alcohol rather than brake fluid...