I know this sounds weird but swmbo has used this method with success.
It works on ink on fabric so it wouldn't hurt to try it.
take some full cream milk and leave it in the sun to go off. Seriously. Must be full cream, must sour by itself, you cant accelerate it with vinegar or anything.
Then strain some of the lumpy bits into your fingers and sit them on the ink. On fabric the ink will actually bleed up into the milk solids. It might take a while though to get it up thru the tile. Not sure how that will go.
rinse with a mild vinegar solution.