Prepare Tomato-Orange Relish.
Mix oil, garlic, and lemon juice.
Rinse tuna, pat dry, and brush all over with oil mixture.
Place tuna on a greased grill 4 to 6 inches above a solid bed of hot coals.
Cook, turning once, until browned on outside but still pale pink in center; cut to test (3 to 5 minutes).
Transfer tuna to a warm platter; season to taste with pepper.
Garnish with parsley sprigs and orange slices.
Spoon a dollop of Tomato-Orange Relish over each piece of tuna;