Prepare the marinade: In a bowl, whisk olive oil, lemon juice, garlic, oregano, paprika, cumin, salt, and pepper.
Marinate the chicken: Add chicken strips, toss well, cover, and refrigerate for at least 30 minutes.
Make yogurt sauce: In a small bowl, combine Greek yogurt, garlic, lemon juice, olive oil, salt, and herbs. Chill until ready to use.
Cook the chicken: Heat a grill pan or skillet over medium-high heat. Cook chicken in batches for 5–7 minutes, turning occasionally, until browned and cooked through.
Warm the bread: Heat pita briefly on a skillet or in the oven until soft and warm.
Assemble wraps: Spread yogurt sauce on pita, add chicken, top with lettuce, tomato, cucumber, onion, and optional feta.
Wrap and serve: Fold tightly and serve immediately.