Slice each chicken breast horizontally to make two even thin cutlets.
Place the sliced chicken in a large gallon zip-top bag and add 3/4 cup olive oil, 1 tablespoon Greek seasoning, 1/2 teaspoon garlic powder, 1 tablespoon lemon juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Seal and shake to coat evenly.
Refrigerate the chicken in the marinade for at least 30 minutes.
Remove chicken from the marinade and lightly oil the grill, grill pan, or large skillet. Heat to medium-high.
Grill the chicken 4–5 minutes per side, or until an instant-read thermometer registers 165°F (74°C). Let rest at least 5 minutes, then slice into pieces.
Meanwhile, make the yogurt sauce: in a small bowl combine 5.3 ounces (about 2/3 cup) Greek yogurt, 1 teaspoon lemon juice, 1 teaspoon Greek seasoning, 1/4 teaspoon garlic powder, and 1/8 teaspoon salt; mix until smooth and set aside.
Warm the pita breads in the microwave for 20–30 seconds or in a toaster oven for about 30 seconds until just warm.
Assemble each pita: add sliced chicken, shredded lettuce, diced cucumber, diced cherry tomatoes, diced red onion, and a drizzle of the yogurt sauce. Roll or fold to serve.
Optional: use a piece of parchment or foil to help keep each wrap together while eating.