Heat large skillet over medium heat and add 1 tablespoon of oil. Break turkey burgers up into small pieces and add pieces to skillet. Add allspice, cumin, and oregano and mix well. Cook 5 minutes to heat through, stirring frequently.
Meanwhile, in a small bowl, combine yogurt, cucumber and garlic powder. Mix well.
Place a piece of lettuce in the bottom of the pita pocket. Spoon turkey mixture onto lettuce in pita pockets and top with yogurt mixture.