Finish the glass tile installation on the rest of the backsplash. Leave space for the liner by laying out the liners with the tiles in a dry layout before you begin installing.
Scoop up a small amount of mortar onto the end of the margin trowel and use it to back-butter the liner. Spread a thin, even amount of mortar onto the back of the liner and press the liner onto the wall next to the glass tiles. Wiggle it slightly into place, and wipe away any excess mortar that may have leaked out from behind.
Let the entire installation dry for a minimum of 48 hours, and then grout the liners with the rest of the tiles. Spread the grout over the entire installation with an epoxy grout float. Let the grout dry for 10 minutes, and then clean off the glass tiles with a damp grout sponge.