In a bowl, combine the chicken strips with olive oil, oregano, garlic powder, salt, and pepper. Toss to coat evenly.
Heat a skillet or grill pan over medium-high heat and cook chicken until golden and cooked through, about 5–7 minutes.
While the chicken cooks, whisk together Greek yogurt, minced garlic, lemon juice, olive oil, salt, and pepper in a small bowl to make the garlic yogurt sauce.
Warm the pita breads briefly in a dry skillet or oven to make them soft and flexible.
Spread a generous layer of garlic yogurt sauce over each pita.
Add cooked chicken, cherry tomatoes, cucumber, and red onion to each pita.
Sprinkle crumbled feta over the fillings and garnish with fresh parsley or dill.
Fold or roll the wraps tightly and serve immediately.