In a medium bowl, combine the sliced chicken breast, 2 tablespoons olive oil, minced garlic, dried oregano, ground cumin, smoked paprika, 1/2 teaspoon salt, 1/4 teaspoon black pepper, 1/4 cup Greek yogurt, and 1 tablespoon lemon juice. Mix well to coat the chicken evenly. Marinate for at least 15 minutes.
Preheat a grill or grill pan over medium-high heat.
Grill the marinated chicken slices for 5-7 minutes per side or until fully cooked and slightly charred. Remove from heat and let rest for 5 minutes.
In a small bowl, prepare the sauce by mixing 1/2 cup Greek yogurt, 1 tablespoon lemon juice, 1 minced garlic clove, 1/4 teaspoon salt, and 1/8 teaspoon black pepper until smooth.
Warm the whole wheat pita breads in a dry skillet or oven for 1-2 minutes until soft and pliable.
To assemble each gyro, place a warm pita on a plate. Spread 2 tablespoons of the yogurt sauce over the center of the pita.
Add a quarter of the grilled chicken slices on top of the sauce.
Top the chicken with 1/4 cup halved cherry tomatoes, 1/4 of the sliced cucumber, 1/8 of the sliced red onion, and 1 tablespoon crumbled feta cheese.
Sprinkle with chopped fresh parsley.
Fold the pita around the fillings and serve immediately.