When the grill is hot, use tongs to swab the grate with a paper towel dipped in vegetable oil. Place the salmon on the hot grill, skin-side up. Let the salmon cook until it has grill marks and the edges look browned, about 3 minutes. Carefully lift each fillet and turn over. Close the lid of the grill and cook about 4 minutes more for thin, wild-caught fillets, longer for farm-raised salmon. When the fish is just cooked through, transfer to a clean platter. Top each fillet with about a quarter cup of salsa, and serve hot.