To prevent that movement from creating cracks in your grout and tile install a crack prevention membrane after the concrete subfloor is clean flat and free of cracks larger than 1 8 inch.
How to remove paint from concrete floor before tiling.
You can either roll on a liquid latex membrane or use a peel and stick crack prevention mat over the entire concrete subfloor.
To remove paint from concrete first sweep the concrete to clean the area you ll be working on.
Spread a thick layer of paint stripper over the paint with a cheap paintbrush.
Take some water and mop the surface to remove any dirt dust or small debris.
Scrub the floor after sweeping give the floor a good scrub to remove any stubborn dirt or persistent stains.
Seal off the area with poly sheeting.
Concrete sealant or paint prevents the adhesive from sticking properly.
Use a paint scraper to scrape up any thick globs of paint that are sticking up off of the concrete.
Use the solution and the scrub brush to clean the floor thoroughly.
Then put on a dust mask gloves and protective eyewear.
Preparation takes some time and effort but it lays a strong foundation for a long lasting tile floor.
Follow your local environmental codes for disposal.
Wear an asbestos rated respirator.
Change clothes before moving into a clean area.
Pour a few tablespoons of degreasing cleaner into the bucket and add about a gallon of warm water to create a cleaning solution.
For more information search the internet for removing asbestos tiles.
Clean the entire room with a damp cloth before removing the sheeting.
You need to clean any paint sealant or glues from the surface of the concrete.
Once you clean all these agents off the top of concrete you can begin preparing the surface.
Even if you tried to strip the paint or even grind it down your floor will be to smooth for a proper adhesion with thinset mortar eventually your floor will fail.
Add 2 to 3 tablespoons of a good degreasing cleanser such as dishwashing soap or trisodium phosphate to a gallon of warm water and scrub the floor with a scrub brush.