Unless you've got a lot of intricate cuts (tough with concrete board) or expect to have a LOT of water on your backsplash on a regular basis, it's probably just simpler to go with backerboard.
I have used a Kerdi-board competitor, Wedi, for a shower and found it very easy to work with. Easy to cut and seal. Comes with sealant (caulk tubes) and fastening bolts (might be tricky to drive in small backsplash places) To avoid flex, you want to use a thicker board. It's pretty strong stuff (particularly for a kitchen backsplash, which shouldn't bear much (any?) weight or pressure.
I have also used the original Kerdi membrane (not the newer board you mention) for a shower. I have a lot of confidence in the quality of the seal with the Kerdi membrane, but it's quite a bit of extra work if you haven't done it before, and is probably overkill for a backsplash (I assume the counter top runs below).
As for cost - my personal opinion is that small jobs are precisely the place to spend the extra money (assuming the quality is better for what you need). If I had to do 100 bathrooms, the added cost of the these newer products would really add up. If I'm doing 1 or 2, then the difference is relatively small.
As a bit of history: The Kerdi membrane (from Schluter Systems) is one of (the?) original products in this space. Wedi board came as a competitive product, eliminating the need to put up drywall and then apply the membrane. Schluter responded with the Kerdi board.
Assuming this is ceramic tile - not glass or stone - and you are going to do the standard mastic installation, if there is only mild damage (for example, a few 4-inch patches ripped off) either just ignore it or use joint compound to fill.
Joint compound is not strong at all. It is pretty crumbly and soft - i.e. it's not plaster, even though builders nowadays use it to skim-coat walls for texture (you can easily gouge it with your fingernail on such installs). So if there are large areas of damage, I would cut out the sections of drywall and replace them. This is not difficult, because although you should still mud-and-tape the joints, you don't need to sand much since you'll be covering it with tile.
Final comment - I wish, on my installation, that we had added 1/4" hardiboard over the sheetrock (with const. adhesive and screws) to stiffen the wall. My wall has the garage door in it, so the wall gets flexed and the grout cracks. Just FYI.
(Adding Fein Multimaster picture, see comment below)
Best Answer
Mirrors get broken. Mirrors lose their silvering on the back. Neither is a likely event, but in this case a very expensive or time consuming one. As a general rule I hate to create situations where fixing it later is difficult.
For this reason were it my project:
Don't attach the mirror to the substrate with adhesive or thinset. I don't know what the chemistry between either and the thin layer of aluminum on the back of the glass would be. If you do removing the mirror will be difficult.
Buy a mirror with holes drilled in it. Buy a set of the cute rosettes and attach the mirror directly to the wall.
Frame the mirror in a complementary wood, and attach THAT to the wall. The outer edge of the frame should be raked about 5 degrees so that it can be removed from the tile when necessary.