Combine beef and seasoning in a large mixing bowl; shape into 4 patties.
Grill patties, covered with grill lid, over mediumhigh heat (350° to 400°) for 5 to 6 minutes on each side or until beef is no longer pink.
Cut off a 2-inch-wide sliver of bread from each pita round to form a pocket. Line each pita with 1 lettuce leaf, 2 tomato slices and 1 red onion slice. Add burger patties. Drizzle each patty with 2 Tbsp. Tahini Sauce, if desired, and sprinkle 1 Tbsp. Feta cheese evenly over each.