Tile question

[Minna Reid]

So I'm about to tile my former garage floor (now a bedroom). It's concrete but has some remnants of a paint job from long ago. The finish is very dull and gone in most areas, but I poured a little water on the floor and it doesnt readily penetrate through the painted spots as it does on the plain concrete. Should I
Just go ahead and use regular mortar and tile over the floor?
Use a latex fortified mortar on the floor?
Attempt to remove whats left of the paint on the floor and then mortar?
Something else altogether?