Thaw fish, if frozen. Rinse fish; pat dry with paper towels. Sprinkle fish with 1/4 teaspoon salt and the pepper. Place fish in a resealable plastic bag set in a shallow dish. In a small bowl combine 1/4 cup of the salsa verde, the mayonnaise, and lime juice. Add to bag. Seal bag and turn to coat. Marinate in the refrigerator 15 minutes.
Meanwhile, in a medium saucepan, heat the oil over medium heat. Add onion, green pepper, and 1/2 teaspoon salt; cook for 2 minutes. Add the garlic; cook 30 seconds more. Stir in broth and the remaining 3/4 cup salsa verde; bring to boiling. Stir in uncooked rice. Reduce heat; cover and simmer for 20 to 25 minutes or until rice is tender.
Remove pan from heat; remove lid. Cover pan with a clean kitchen towel; replace lid. Let stand for 5 minutes to let the towel absorb any excess moisture. Remove lid and towel. Add pineapple and cilantro, fluffing with a fork; keep warm.
For a charcoal or gas grill, place fish on the greased rack of a covered grill directly over medium heat. Grill for 4 to 6 minutes per 1/2-inch thickness of fish or until fish begins to flake easily when tested with a fork. Serve fish with pineapple green rice, tomato wedges and lime wedges.