If your tiles are unglazed "quarry" tiles or similar, we may have a bit of a problem, but if not, you could try a "heavy" solvent.
Tar-like deposits can be removed (slowly) with greasy things like butter or similar.
"Baby lotion" - that pink gloopy stuff - is an emulsion of oil and water. I use it to get filthy grease off my hands. Not very butch, but there we are!
Hope this helps!
Years of doing mucky things.