Roll mushroom caps in olive oil. Over high heat, grill both sides of the mushrooms until the mushroom is soft and cooked through (about 8 to 10 minutes). Remove the mushrooms from the grill.
Fill each mushroom with a sprinkle of green onions and a few pieces of flaked smoked salmon. Return stuffed mushrooms to a low grill or the warming rack. Close lid of grill and cook until the salmon is hot (about 4 to 5 minutes). Remove from grill.
Place a dollop of horseradish mayonnaise on top of each stuffed mushroom. Serve immediately.