Cut the patties in half. In a small bowl, thoroughly mix the mayonnaise with the dill, pepper to taste, and lemon zest.
Place the halved patties on the work surface and spread evenly with the mayonnaise. Place the salmon slices on top, side by side.
Roll up the pita halves tightly, starting at the narrow end, but do not allow the mayonnaise to ooze out the sides. Wrap individually in plastic wrap and refrigerate for 1 hour. Before serving, remove the plastic wrap and cut the rolls crosswise into slices about 2.5 inches thick using a serrated knife. Arrange on a platter and serve immediately.