Season shrimp on both sides with seafood seasoning. Grill or pan fry for about 2 minutes per side over medium heat until opaque. If steaming, cook until opaque, about 3 minutes in a covered pan. Chill cooked shrimp.
In a medium-sized bowl, cream together mayonnaise, Chai Thai Teriyaki Sauce, parsley. Stir in chilled shrimp, celery and onion. Serve chilled.