The Dremmel would take way too long. I would suggest a cement saw and cut a square, use an impact drill to break up the square you cut out, then patch the hole.
Alternatively you could use an impact drill to drill out the previous patch and there are various tips you could use for a sawzall that would chip out the rest.
Didn't realize it was a tile. Yep take out the tile and put a new one down. Assuming he has any left. Otherwise a similar tile or a patch would stand out the same.