In a large bowl, combine the chicken strips with olive oil, garlic powder, smoked paprika, ground cumin, dried oregano, salt, and pepper. Mix well to ensure the chicken is evenly coated with the spices.
Preheat a grill pan or skillet over medium-high heat. Once hot, add the marinated chicken strips and cook for about 5-7 minutes, or until they are golden brown and cooked through, stirring occasionally.
While the chicken cooks, prepare the pita bread by warming them in a pan or microwave for a few seconds until pliable.
Once the chicken is done, remove it from heat.
To assemble the gyros, take a warmed pita bread and spread a generous amount of tzatziki sauce on it.
Top the sauce with a portion of the grilled chicken, diced tomatoes, cucumber, red onion, and chopped parsley.
Roll the pita tightly, folding in the edges to contain the filling.
Serve immediately with a wedge of lemon on the side for an extra burst of freshness.