Spread the mortar with the flat edge of the trowel then groove.
How to install tile backsplash on uneven wall.
If existing tiles are beyond repair remove the tile and install a piece of wallboard in its place.
A professional installer would use a pair of scribes to transfer the contour of the wall onto the top edge of the counter top then use a circular saw or a belt sander to take off the area of the backsplash where your wall is bowed out.
Wash the wall with tsp tri sodium phosphate or an ammonia based cleaner to remove any grease or oil.
Hold a tile at this spot accounting for a 1 8 inch expansion gap.
Mark the two sides of the wall using the painter s tape where the backsplash should.
1 4 inch is not too much to take off provided your cabinets do not measure anymore than 24 from wall to front of face frame.
Use tile spacers if necessary to keep the tile lines straight in the layout.
Do not grout the bottom seam where the tile meets the countertop you ll want to use caulk in that seam.
Ready to get started.
If your cabinets are farther than 24 away from wall then you won t have excess on backsplash to trim off.
While you volunteered to set tiles is repairing rebuilding the wall something you even want to deal with.
Place the mosaic sheets along the wall.
Backsplash installation in 15 steps.
Learn how to install a tile backsplash.
Shop for tile.
That is what i would do so it could be painted i would not even try to tile over the patch job you described.
Back buttering back buttering is a trick used for tiles of uneven thickness like ungauged slate or handmade tiles extremely large tiles or for tiles being installed on an uneven surface.
Mark the wall at the top of the tile.
Clean the wall thoroughly with the cleaner to remove any grease or other debris.
Use the float to take off any excess grout then allow the grout to set for 10 minutes.
Shop for grout and mortar.
Secure the drop cloth on the counter using the painter s tape covering the entire work area.
Then use a level to extend the line along the work area.
Hold the float at a 45 degree angle as you work the grout into the seams.
This ensures the tile adhesive secures to the surface.
Follow the lines you made when the tiles were dry fit to the wall.
Like bill pointed out you are unlikely to end up with a flat enough surface to get a good tile job unless you use very small tiles.
First use a level to find the lowest point of the countertop.
Apply grout with a rubber float working diagonally across the tile.
Spread thinset mortar on the bottom center of the wall.