Place beef, onion, 1/4 cup parsley, 11/2 teaspoons salt, 1/2 teaspoon pepper and cumin in a mixing bowl and mix together with your fingers. Lightly wet hands with cold water and form meat into 12 patties about 2 inches in diameter and 1/2- inch thick. Place patties on baking sheet lined with plastic wrap and refrigerate, covered, until ready to grill.
Place tomatoes, olives and 3 tablespoons parsley in nonreactive bowl and toss to mix. Squeeze in juice of 1 or 2 lemon wedges. Place remaining wedges in a dish and set aside for serving. Season tomato-olive relish with salt and pepper to taste (it should be highly seasoned).
Set up grill for direct grilling and preheat to high. When ready to cook, brush and oil the grill grate. Place patties on hot grate and grill until crusty and brown and cooked through, 2 to 4 minutes per side for medium to medium-well.
To serve, place patty on pita bread wedge. Squeeze lemon juice on top and spoon tomato-olive relish over it.