In a medium bowl, combine olive oil, garlic, oregano, paprika, cumin, lemon juice, salt, and black pepper. Mix everything well until the marinade becomes fragrant and smooth. Add the chicken strips and coat them thoroughly before letting them marinate for at least 20 minutes.
While the chicken marinates, stir together Greek yogurt, grated garlic, lemon juice, olive oil, and fresh herbs in a small bowl. Mix until creamy and well combined. Place the sauce in the refrigerator so the flavors can develop while you prepare the rest of the recipe.
Wash and slice the tomatoes, cucumber, onion, and lettuce into bite-sized pieces. Keeping the vegetables fresh and crisp makes the wraps taste lighter and more refreshing. I like to chill the vegetables slightly before assembling for extra crunch.
Heat a grill pan or skillet over medium-high heat. Add the marinated chicken strips and cook for about 5 to 6 minutes, turning occasionally until golden brown and fully cooked. The edges should become slightly charred while the inside stays juicy.
Place the pita bread on a dry skillet for about 20 seconds per side until soft and flexible. Warm bread folds much easier without cracking. You can also wrap the pita in foil and warm it in the oven for a few minutes.
Spread a generous layer of garlic yogurt sauce over each warm pita. Add grilled chicken, lettuce, tomatoes, cucumber, onion, and feta cheese evenly across the center. Finish with fresh parsley and another drizzle of yogurt sauce for extra flavor.
Fold the sides inward and roll the pita tightly into wraps. Slice each wrap diagonally for a beautiful presentation. Serve immediately while the chicken is warm and the vegetables remain crisp.