In a large bowl, combine the halved cherry tomatoes, diced cucumber, diced red bell pepper, and finely chopped red onion.
Stir in the Kalamata olives and crumbled feta cheese into the vegetable mixture, gently mixing to combine without breaking the feta too much.
In a small bowl, whisk together the olive oil, red wine vinegar, chopped oregano, salt, and pepper. Pour the dressing over the salad and toss gently to coat all the ingredients evenly.
Take one whole wheat pita pocket and carefully open it up. Fill it with a generous amount of the Greek salad mixture, making sure to include olives and feta in each pocket.
Repeat the stuffing process for the remaining pita pockets.
If desired, top the stuffed pita pockets with a sprinkle of fresh parsley before serving.