Begin by placing the sliced chicken into a mixing bowl. Add the Greek seasoning, kosher salt, and ground black pepper. Toss the chicken until it's well-coated with the spices. Let it marinate for at least 15 minutes at room temperature.
Heat a skillet or grill pan over medium heat. Once hot, add the marinated chicken strips. Cook for about 5-7 minutes, flipping occasionally, until the chicken is golden brown and cooked through. In the last few minutes of cooking, add the sliced sweet onion to the skillet. Sauté until the onions are soft and slightly caramelized, about 3-4 minutes.
While the chicken and onions are cooking, prepare the whole wheat pitas by cutting them in half and gently opening them to create pockets. If you prefer, you can warm the pitas in a dry skillet for about a minute on each side.
Start by placing a few torn romaine lettuce leaves at the bottom of each pita pocket. Next, add a generous portion of the cooked chicken and caramelized onions. Top with halved grape tomatoes, sliced kalamata olives, and a sprinkle of low-fat feta cheese.
Carefully hold the pita pockets together and serve immediately while everything is warm.