For relish, drain artichokes, reserving marinade. Coarsely chop artichokes. In a medium bowl, combine artichokes, reserved marinade, tomatoes, olives, green onions, vinegar, garlic, and black pepper. Cover and chill in the refrigerator for at least 2 hours or up to 4 hours.
At least 1 hour before grilling, soak wood chips in enough water to cover. Drain before using. Trim fat from steaks. Sprinkle steak seasoning evenly over steaks; rub in with your fingers.