Prepare barbecue (medium-high heat). Stir tomatoes, olives, onion, 2 tablespoons oil, and mint in small bowl to blend.
Brush 1 side of each pita with remaining 2 tablespoons oil; place pitas, oiled side down, on grill. Cook until lightly charred, about 2 minutes. Turn pitas over; top with tomato mixture, spreading almost to edges.
Sprinkle with cheese.
Cover barbecue and grill pitas until topping is warm, about 2 minutes.
Transfer pitas to plates and serve.
To pit an olive easily, simply crush the olive with the side of a chef's knife and pop out the pit.