EVERYONE has given him the wrong advice here. What is the matter with you lot.
You don't have to remove any paint, or waste any money on Ditra mat.
Just spread out a layer of sand about 1cm thick over the floor. Then re-screed it 10 cm thick, and use some reinforcing matting (stainless steel). Leave to dry for 10 weeks. They tile directly to it. The sand will act as a de-coupling membrane (same as Ditra, but much cheaper). This is how it was done for the last 3,000 years.
You see, there is ALWAYS more than one, two, or even three, ways to skin a cat... :lol: