Heat the grill to about 400°F (medium-high) and clean the grates; oil the grates or brush salmon with oil to prevent sticking.
Pat salmon fillets dry, rub each with 1 teaspoon olive oil, then season both sides with Greek seasoning.
Place salmon on the hot grill, skin-side down, and cook 5–6 minutes without moving.
Carefully flip the fillets and cook the other side 4–5 minutes more, or until the internal temperature reaches 140°F and fish flakes easily.
While the salmon cooks, combine the Greek salsa ingredients in a bowl and gently toss to combine.
Serve the grilled salmon topped with Greek salsa, garnish with fresh parsley and a lemon wedge, and offer tzatziki on the side if desired.