Preheat the grill or grill pan over medium heat.
In a mixing bowl, combine olive oil, garlic powder, paprika, salt, and black pepper. Coat the chicken breasts with the mixture.
Place the chicken on the grill and cook for about 5 minutes on each side, or until the internal temperature reaches 165°F (75°C). Remove from heat and let it rest for a few minutes.
While the chicken is resting, prepare the sauce by mixing Greek yogurt, mayonnaise, lemon juice, and chopped parsley in a bowl. Stir until well combined.
Slice the grilled chicken into strips.
To assemble the wraps, lay a tortilla flat and spread a generous amount of the sauce on it.
Add a layer of lettuce, diced tomatoes, sliced cucumbers, shredded cheese, and then the grilled chicken strips.
Roll the tortilla tightly around the fillings, tucking in the sides as you go. Repeat for the remaining tortillas.
If you prefer, wrap the grilled chicken wraps in aluminum foil to keep them warm and for easier handling.