Make yogurt sauce: Drain yogurt in a sieve lined with a dampened paper towel set over a bowl 30 minutes. Transfer drained yogurt to a small bowl and stir in garlic paste and mint.
Make burgers: Prepare grill. Handling lamb as gently as possible, in a bowl combine lamb with feta and olives and form into six 1-inch-thick patties. Season burgers lightly with salt and pepper to taste and grill on an oiled rack set 5 to 6 inches over glowing coals 7 minutes on each side for medium-rare.
Transfer burgers to pita pockets and top with tomatoes, bell peppers and onion. Serve burgers with yogurt sauce.