Combine olive oil, yogurt, lemon juice, garlic, and spices in a bowl. Mix thoroughly until smooth. Coat chicken evenly and let it marinate for at least one hour or overnight.
Heat a skillet or grill pan over medium-high heat and cook marinated chicken. Turn occasionally until cooked through and nicely browned. Rest chicken briefly before slicing.
Slice cooked chicken into thin strips after resting. This keeps juices inside the meat. Thin slices make wrapping and serving easier.
Whisk mayonnaise, yogurt, lemon juice, garlic, olive oil, and salt until smooth. Chill briefly to thicken flavors. Adjust garlic or lemon to taste.
Place sliced chicken on warm pita with vegetables and drizzle garlic sauce. Wrap tightly for easy eating. Serve immediately while warm.
You can toast assembled wraps lightly in a pan for extra texture. This step adds crispness without drying fillings. Serve hot for best flavor.