Step 1

Place Greek yogurt, cucumber, dill weed, 2 cloves garlic, white vinegar, 1 teaspoon lemon juice, 1 tablespoon olive oil, salt, and black pepper in a blender. Blend until smooth; set aside.

Step 2

Whisk together 4 cloves minced garlic, juice of 1 lemon, red wine vinegar, 2 tablespoons olive oil, and oregano in a large glass or ceramic bowl. Season to taste with salt and black pepper.

Step 3

Stir in chicken strips and toss to evenly coat. Cover the bowl with plastic wrap and marinate in the refrigerator for 1 hour.

Step 4

Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.

Step 5

Remove chicken from the marinade and shake off excess. Discard the remaining marinade. Place chicken on a large baking sheet.

Step 6

Broil the chicken in the preheated oven until lightly browned and no longer pink in the center, 2 to 4 minutes per side.

Step 7

Transfer cooked chicken to a plate and allow to rest for 5 minutes.

Step 8

Heat 1 teaspoon olive oil in a large skillet over medium heat; place each pita bread into the skillet until warm and soft, about 2 minutes per pita.

Step 9

Serve warmed pita bread topped with chicken strips, yogurt sauce, tomatoes, onion, and lettuce.