Combine olive oil, lemon juice, minced garlic, cumin, paprika, salt, and pepper in a bowl and coat the chicken thighs thoroughly.
Cover and refrigerate the chicken for at least 1 hour or overnight to marinate.
Preheat your grill to medium-high heat.
Let the marinated chicken rest at room temperature for 10 minutes before grilling.
Grill the chicken for 6 to 7 minutes per side until the internal temperature reaches 165°F (75°C).
Mix mayonnaise, yogurt, minced garlic, lemon zest, salt, and pepper together until smooth to prepare the garlic sauce.
Allow the grilled chicken to rest for 5 minutes before slicing into strips.
Assemble the shawarma wraps by placing chicken strips in warm pita bread, topping with fresh vegetables and drizzling generously with garlic sauce.