- Rinse hen quarters under cold running water; pat dry with paper towels.
- Combine 1/3 cup less sodium teriyaki sauce and lemon juice; pour over quarters in large plastic food storage bag. Press air out of bag; close top securely. Turn bag over several times to coat all pieces well. Refrigerate 8 hours or overnight, turning bag over occasionally.
- Combine remaining 2 Tbsp. less sodium teriyaki sauce, apricot preserves and ginger in small saucepan. Heat and stir just until preserves melt.
- Cook hens on grill, 8 to 10 inches from medium-hot coals, 40 to 45 minutes, or until no longer pink next to bone, turning pieces over frequently. Brush pieces with apricot mixture during last 5 minutes of cooking time.