Heat gas or charcoal grill. In shallow bowl, mix tomato, cucumber and vinaigrette. Let stand while preparing patties.
In medium bowl, combine ground beef, onion, Italian seasoning, garlic-pepper blend and salt; mix well. Shape mixture into 4 oblong patties, about 1/2 inch thick.
When grill is heated, place patties on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cover grill; cook 11 to 13 minutes or until meat thermometer inserted in center of patties reads 160°F., turning once. During last 1 to 2 minutes of cooking time, place cheese on patties; cook until melted.
Place cheese-topped patties in pita bread halves. Spoon tomato-cucumber mixture into bread halves with patties.