Preheat a grill.
Place the red snapper fillets in a shallow dish and reserve. In a small bowl, combine lime juice, ginger, pepper, and olive oil. Pour the mixture over the fish and let sit for 15 minutes.
Grill the fish over medium heat until the flesh is cooked through and opaque, about 4 minutes per side, depending on the size of the fish. Top with tropical fruit salsa and serve.