Heat grill. In small bowl, combine all sesame-ginger mayonnaise ingredients; blend well. Set aside or refrigerate until ready to use.
Place 1 chicken breast, boned side up, between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound chicken with flat side of meat mallet or rolling pin until about 1/2 inch thick; remove wrap. Repeat with remaining chicken breast halves. Brush flattened chicken and pineapple slices with about 2 teaspoons of the teriyaki baste and glaze. Refrigerate until ready to use.
When ready to grill, place chicken on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 8 to 10 minutes or until chicken is fork-tender and juices run clear, turning once and brushing with remaining 2 teaspoons teriyaki baste and glaze. To toast rolls, place cut side down on grill during last 1 to 2 minutes of cooking time. Place pineapple slices on grill; cook 1 minute, turning once.
Spread half of sesame-ginger mayonnaise evenly onto bottom halves of rolls. Top with lettuce, chicken, remaining mayonnaise and pineapple slices. Sprinkle with green onions. Cover with top halves of rolls.