[pb4ugo]

Sounds like non-sealed/glazed tile? I've used straight caustic soda (the basis for CLR) before to clean my grout and never had it discolor my glazed tile.

Anyways, there are two different trains of thought I'd use in your situation. The first is to use a little more CLR to re-activate what is sitting there in the material. After its wet with CLR, you'd wipe it all up with a plenty wet rinse. And rinse, and rinse, and rinse.

Even after all that rinsing, there is likely to be some discoloring residue. By now it should be all chemical residue since all the dirt has been rinsed away. Since CLR is a basic substance (lye/caustic soda/sodium hydroxide) you will need a little acid to neutralize. By now it should be weak enough in your tile to use something the likes of lemon juice to achieve neutralization.