I found the Grout Grabber to be all but useless. First, a proviso: my grout was extremely nasty - very hard, more like stucco actually. Sure, this tool removed some of it, though not quickly and not without a bunch of blade changes. Maneuvering the large sawzall around the enclosed spaces that were tiled was pretty tedious too. After struggling with this for a few hours and getting a moderate amount of work done, a buddy recommended a Rotozip, and loaned me his. A quick trip to the hardware store for a diamond blade and I was in business. The Rotozip did the trick. It was fast, went through the grout like my circular saw goes through wood. It also went through the chicken wire that was holding the mortar in place, throwing off some lovely (but harmless) sparks.
Note that I didn't use the carbide grout bit, which I tried and found to be useless. I used a circular diamond blade intended for tile, cement and so forth. Note as well that this blade isn't recommended for the speed of the cheaper Rotozip, but that's what I had and it worked.
Anyway, the combination of the Rotozip RTM01 with RotoZip ZM101 and the Dry Diamond blade worked like a dream. There is a more expensive Rotozip with adjustable speed that should work as well and perhaps be safer.