My old worn out white bath tile is now black because the finish is worn so any dirt goes right in. It now looks like it's stained in spots even after mopping. I'm not ready to replace it until we are going to sell the house. Any suggestions in the interim. I do have pets, but will gladly rinse any solution that will work. Thanks

A sander either a drum, or a buffer. Thinset is not there to "bond" the CBU, it is there to fill voids and add support, over minor low and high areas, so the CBU doesn't flex.

I had to do that job once, working for a remodeller when I was in high school. The guy I was working for had me use a propane torch with a fan tip on it, warming the flooring and keeping a putty knife hot to melt through the adhesive and gradually lift the flooring, in little pieces. A solvent may help clean up residue after most of the thick stuff has been mechanically removed.

I clean our Legion every 2 weeks. They replaced their previous linoleum floor with a laminate flooring. Both floors are light coloured an I was always on my hands and knees getting the black marks off. I used a Mr Clean eraser at first but then stopped, it left white marks, not residue from the eraser itself, but it was taking the coating of the floor off. Even when using an eraser on the walls to remove scuff marks, I can see pale spots. I really don't like using them. What took it off quick and easy was the blue easy-off pad. A couple of swipes and immediately wipe off the blue soap and it was clean.