The olive relish that tops the steak is also delicious served on grilled Italian bread.
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.
To grill, in a grill with a cover, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Sprinkle the drained wood chips over the coals. Place steaks on the grill rack over drip pan. Cover and grill steaks for 16 to 20 minutes for medium-rare doneness or until an instant-read thermometer inserted in steak registers 145 degree F. (Or for 20 to 24 minutes for medium doneness or until an instant read thermometer inserted in steak registers 160 degree F).
Serve steaks with relish. Makes 8 servings.