Make the quick sauce. In a small bowl, mix Greek yogurt, lemon juice, garlic, a pinch of salt, and a drizzle of olive oil. Stir until smooth.
Taste and adjust with more lemon or salt.
Season the chicken. Toss the cooked chicken with olive oil, cumin, smoked paprika, salt, and pepper. If your chicken is cold, warm it in a skillet for 2–3 minutes to bloom the spices.
Prep the veggies. Slice the cucumbers, tomatoes, and red onion. Chop the herbs and shred the greens.
Keep everything in small, even pieces so the wrap holds together.
Warm the pitas. Heat pitas in a dry skillet for 30–60 seconds per side, or wrap in a damp paper towel and microwave for 15–20 seconds. Warm pitas fold without tearing.
Assemble. Spread a spoonful of sauce inside each pita or over the center if using pocketless pitas. Layer greens, chicken, cucumbers, tomatoes, red onion, and a sprinkle of feta and herbs.
Wrap it up. If using pocket pitas, tuck filling into the pocket.
For pocketless, fold the sides over the filling, then roll from the bottom up. A piece of parchment or foil helps keep it snug.
Finish and serve. Add a final drizzle of sauce or a squeeze of lemon. Serve right away with extra veggies on the side.