Steep tea bags in 1 cup boiling water, 5 minutes; discard bags. Add other 1 cup water, soy, garlic to tea.
Loosen skin around chicken breasts and legs. Place chicken in food-storage bag. Add tea mixture to bag; push out air; seal. Refrigerate 1 to 4 hours.
Prepare grill with hot coals around sides. Place foil drip pan in center.
Remove chicken from plastic bag; pour marinade into drip pan. Place neck and gizzard in pan. Position grill rack 6 inches above coals. Place chicken on grill rack over center of drip pan.
Grill, covered, 2-1/2 to 3 hours or until meat thermometer inserted in thigh registers 175°F. Add briquettes to each side of grill every 50 to 60 minutes to maintain constant heat. (You may add soaked hickory chips after first hour of cooking.)
Combine jam, ginger, soy sauce and sesame oil in small bowl. Brush over chicken during last hour of cooking.
Let chicken stand at least 20 minutes before carving.
Discard neck and gizzard from pan. Pour drippings into liquid measure. Skim off fat. Add water to equal 3 cups. Pour into saucepan with jam and honey. Simmer. Combine cornstarch, 1/4 cup water and salt in small bowl. Stir into saucepan. Simmer, stirring, 2 to 3 minutes or until thickened. Remove from heat. Stir in lemon juice. Serve with sliced chicken.