Warm the olive oil in a large skillet over medium heat.
Add the minced garlic and cook it for about a minute until you smell its fragrance.
Toss the chicken strips into the pan, season with dried oregano, salt, and pepper, then cook for 6 to 8 minutes until the chicken has a nice browned finish and is fully cooked.
Turn the heat down to low, sprinkle the shredded mozzarella cheese evenly over the chicken, cover the pan, and let the cheese melt smoothly for around 2 to 3 minutes.
Heat the low-carb tortillas gently in another pan or microwave just until warm.
Distribute the cheesy garlic chicken evenly among the tortillas.
Add chopped fresh parsley on top, roll the wraps firmly, and serve right away.