In a large bowl, combine olive oil, minced garlic, oregano, paprika, cumin, lemon juice, salt, and pepper. Add the chicken strips and toss to coat completely. Let marinate for at least 15 minutes, or up to 2 hours in the fridge for deeper flavor.

In a medium bowl, combine Greek yogurt, grated cucumber (make sure to squeeze out excess water), crumbled feta, fresh dill, lemon juice, and minced garlic. Mix well and season with salt and pepper. Refrigerate until ready to serve.

Heat a large skillet or grill pan over medium-high heat. Add the marinated chicken strips and cook for 5 to 6 minutes, turning occasionally, until golden brown and cooked through (internal temperature 165°F). Remove from heat and let rest.

Warm the pita breads in a dry skillet for about 30 seconds per side, or wrap in foil and heat in a 350°F oven for 5 minutes. You can also microwave them wrapped in a damp paper towel for 20 seconds.

While the chicken rests, arrange your toppings: slice the tomatoes, onions, and cucumbers. Wash and dry the lettuce. Have everything ready for easy assembly.

Lay a warm pita flat and spread a generous layer of the creamy feta tzatziki down the center. Add lettuce, chicken strips, tomatoes, cucumbers, red onion, and any other toppings. Drizzle with extra tzatziki. Fold the bottom up and sides in to create a wrap. Serve immediately.