Preheat oven to 450°.
Heat oil in a large nonstick skillet over medium-high heat. Add onion and bell pepper; cook 2 minutes or until tender. Add turkey; cook 3 minutes. Add tomato, 2 tablespoons parsley, tomato paste, and next 3 ingredients (through allspice) to pan; reduce heat to medium. Cook 5 minutes or until liquid almost evaporates.
Place pitas on a baking sheet. Combine low-fat yogurt, salt, black pepper, and red pepper in a small bowl; spread evenly over pitas. Divide turkey mixture evenly over pitas; sprinkle evenly with remaining 2 tablespoons parsley. Bake at 450° for 5 minutes; serve immediately.