Do you have a 4 inch angle grinder if your carefull you can use that on the tile, score a few lines, you dont go right through just 1/2 to 3/4 then you can gently tap it out with a chisel or old screwdriver.
as for removing grout, sometimes the tools to wide and better to use a stanley knife blade.
as for removing grout, sometimes the tools to wide and better to use a stanley knife blade.