Prepare a charcoal grill with hot coals, or heat a gas grill to high, or heat an oven broiler.
Mix 2 tablespoons oil, anchovy and garlic in bowl. Add tomato, olives, capers, basil, thyme and pepper.
Rinse tuna steaks and pat dry. Brush with remaining 2 tablespoons olive oil. Sprinkle with salt.
Grill or broil tuna 3 minutes each side for medium-rare or until desired doneness. Place on 4 plates. Spoon tomato mixture over tuna. Garnish with thyme.