Step 1: In a medium bowl, combine the sliced chicken with olive oil, 2 tbsp lemon juice, 2 minced garlic cloves, oregano, 1/2 tsp salt, and 1/4 tsp pepper. Toss to coat the chicken evenly. Cover and refrigerate for at least 30 minutes, or up to 2 hours for best flavor.
Step 2: While the chicken marinates, prepare the garlic yogurt sauce. In another bowl, combine Greek yogurt, grated and squeezed dry cucumber, 1 minced garlic clove, 1 tbsp lemon juice, fresh dill, and salt and pepper to taste. Stir well. Cover and refrigerate until ready to serve.
Step 3: Heat a large skillet or grill pan over medium-high heat. Add the marinated chicken strips and cook for 5-7 minutes, stirring occasionally, until cooked through and lightly browned. Alternatively, grill on an outdoor grill until done.
Step 4: Warm the pita breads. You can do this in a dry skillet for 30 seconds per side, in the microwave for 10-15 seconds, or briefly on the grill.
Step 5: To assemble the wraps, spread a generous amount of garlic yogurt sauce on each warm pita. Top with cooked chicken, chopped tomatoes, chopped cucumber, red onion, Kalamata olives (if using), shredded lettuce, and crumbled feta cheese (if using).
Step 6: Fold or roll the pita to create a wrap and serve immediately.