Grill turkey on the rack of an uncovered grill directly over medium heat for 12 to 15 minutes or until turkey is tender and no longer pink, turning once. Set aside half of the salad dressing; brush remainig dressing on the turkey during the last 5 minutes of grilling.
Meanwhile, stir together olive oil and garlic. Using a pastry brush, brush oil mixture over one side of pita bread. Place pita bread, brushed sides down, over medium heat. Grill for 2 to 3 minutes or until toasted.
To assemble, place lettuce leaves on grilled side of one pita bread half. Top with turkey, tomatoes, and, if desired, avocado; drizzle with reserved salad dressing. Top with shaved Parmesan cheese. Add a pita bread half to top of each. Makes 4 servings.