In a large bowl, combine the egg, bread crumbs, onions, 2 tablespoons teriyaki sauce and onion powder. Crumble turkey over mixture and mix well. Shape into four 3/4-in. thick patties.
Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Grill patties, covered, over medium heat or broil 4 in. from the heat for 6-8 minutes on each side or until a thermometer reads 165° and juices run clear. Brush with remaining teriyaki sauce during the last 5 minutes.
Grill or broil pineapple slices for 3-4 minutes on each side or until heated through. Serve burgers and pineapple on buns.