I have a famous and tedious answer that might or might not work....whenever I have to remove something like that I use a very high quality chisel and slide it over the surface. On a good quality tile, it will (if carefully done) slip under the contact cement and cut it from the base. It might or might not work, but I wanted to share that option. I've used this trick for grout, glues, etc., and so far, so good...and not ruined the surface but you have to remember to be careful to keep the blade flat on the surface you want, and slowly try to push it under without digging in.