Replacing old cabinet and Formica countertop with new cabinet and quartz counter. New cabinet and top will be 4 inches taller than what is there now. Problem: 2 ceramic soap holder and toothbrush holder that are attached to the tile. We cannot afford a full-out renovation and were not planning to remove the existing tile. When installed the new cabinet/countertop will end up about half-way/middle of these holders. Suggestions for the best way to remove holders without damaging tiles are welcome.