I would use a high quality 2 inch wide painter's masking tape on the areas of the walls you wanted to put the tiles up first, trace the outline of the tile on the masking tape, and then use this tool:
To remove the masking tape just inside the outline mark. Hold the tool tight to the wall inside the outline mark and pull the tape off so that the tape is cut along the sharp edge of the tool. The result will be a square or rectange of painter's masking tape on the wall just a little smaller than the size of the tile.
Now, stick your tiles up with 1/16" thick double sided mounting tape (traditionally used for mounting mirror tiles on walls back in the 60's and 70's). Stick the tile onto the painter's masking tape so that you can gradually pry the tiles off the double sided mounting tape, and then pull the painter's tape off the wall to remove the tiles without harming the walls.
The pictured tool is sold in home centers as a "wallpaper scraper" which is completely ridiculous because it's so sharp that the only wet surface you could conceivably use it on MIGHT be strong lime putty based plaster walls to remove wallpaper. If you use it anywhere near wet drywall paper, it'll butcher the surface paper of the drywall. Longer and stronger versions of the same tool are sold in places that sell flooring installation supplies, and the Installations Manager at any carpet retailer will know who sells flooring installation supplies in your area.
If you look closely at that tool, you will notice a small hole at the BACK of the blade. Yes, in that picture the blade is installed backwards. They do this intentionally so that store employees and customers don't hurt themselves handling these tools cuz the blades in them are sharp as a razor. So, be careful using it.