Combine mayonnaise, garlic powder, and chopped parsley in a small bowl to create the garlic aioli base.
In a mixing bowl, coat chicken strips with olive oil, minced garlic, oregano, salt, and pepper.
Heat a heavy-bottomed skillet over medium-high heat; sear chicken strips for 6 to 8 minutes or until internal temperature reaches 165 degrees Fahrenheit.
Lay flour tortillas flat and apply 1 tablespoon of garlic aioli to the longitudinal center of each.
Distribute cooked chicken strips and the cheese blend evenly across the four tortillas.
Fold the lateral ends of the tortillas inward and roll tightly to secure the filling.
Place the assembled wraps seam-side down in the skillet over medium heat for 2 minutes per side until the tortilla is crisp and the cheese is fully melted.