Brush fillets with olive oil; sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper, and place in a lightly greased grill basket.
Grill, covered with grill lid, over medium-high heat (350° to 400°) 8 to 10 minutes on each side or until fish flakes with a fork. Cool fish and flake.
Stir together mayonnaise, lemon juice, remaining 1/4 teaspoon salt and 1/4 teaspoon pepper in a large bowl; add fish, celery, and next 4 ingredients, tossing lightly. Cover and chill 30 minutes. Serve on lettuce-lined plates; add tomato wedges if desired.