Sometimes the fit between a tile backsplash and a granite countertop is poor and a gap of up to 1/2 inch may run along the back of the countertop. Replacing either the backsplash or the granite may be unreasonable and expensive. The trick is to hide the gap in a way that looks intentional. One way to accomplish this is to use a decorative tile that combines the look of the granite and the tile. This becomes a transition tile that will suggest it was intended for just that purpose.
Clean the backsplash and the countertop in the area of the repair, using a degreasing cleanser and water. Remove any caulking from the gap with a utility knife.
Attach your trim pieces to both the tile and the granite. Use a tile adhesive rather than thinset as the thinset may not have enough to grab onto. Adhesives designed for tile on tile and tile on glass will work. Space between the tiles the same as the backsplash grout lines. Let the adhesive dry completely.
Mix a small amount of grout in a bowl and apply it to the grout lines, using a small putty knife or a plastic bag dispenser. Fill in all the grout gaps and holes with grout. Often it is easier to press the grout in place with your fingers around fancy trim shapes. Keep the grout off the faces of the tiles as much as possible. Begin cleaning the grout off the tile after 15 minutes.
Wipe and clean the grout with a sponge. Remove all the excess grout. Keep cleaning until all of the grout and haze are cleaned off. Allow the grout to dry for 24 hours before using the area.