The brown paper you are seeing is probably the backing that held the sheets of tile together. This is common for the smaller tiles that are around an inch square. It aided in the speed of the installation.
The mastic that holds the tile to the wall will be the next layer, then the drywall.
There really is no good way to quickly this without hurting the drywall. It is very rare that we even try to save that drywall due to the labor intensiveness it requires.
Your best bet is to score the drywall at the top of the counter top or cabinet (depending on what you have removed or are going to remove), score the drywall under the upper cabinets and take out the drywall with the tile still on it.
If you are doing it yourself, the speed of replacing this depends on your skill level. A typical kitchen backsplash should take about 2 to 3 hours to replace the drywall, then it will need to be taped and mudded back together, which varies widely on the time required.
In regard to your time constraint, there is the option of overlaying a new layer of tile over the existing, but this is not the best option because it requires specific application knowledge and special edging to keep it from looking make-shift.