I know I do not post here much, but I have to comment on this one. You are all working way to hard.
All you need to use is a rub brick;http://www.marshalltown.com/Products.aspx?D=200&S=219
There are times power tools are not the correct answer.
Thinset is not as hard as brick mortar or concrete. If you wet to surface as you rub it will create a slurry that can be washed off. You can use the brick dry also, it will kick up very little dust. The dust it produces can be vacuumed up when you are complete. Also try wetting the surface and just use a scraper, thinset is not water proof, and will soften when wet. Do not soak the floor!!!!!!!!!!!!!!!!!!!!!
Either way you must wash the floor prior to any other products being used.
As for the mat it is repairable in place if need be. You should put a tatletale on the leads just to be certain it has not been damaged, it will alert you if you damage it during the next phase; (there are others on the market, this is the one I use)http://www.nuheat.com/products/accessories/matsense-pro.html
On my installs, I always pour self leveling compound over the elements, then Ditra, then tile. Most floors need some leveling work and thinset should never be used as a leveling product. The SLC also protects the elements from possible trowel damage.
Two to three hours you will be done.
By the way there should be no power to the mat at this point, not enough mass to keep it from over heating.
Once you're done you will really enjoy the floor.
I'll go back to sitting in the corner now, soaking up all the [festool] knowledge that is presented here.