Place all of the ingredients for the salsa verde in a mixing bowl. Stir to combine. Taste and season with additional lemon juice and/or salt if necessary. You may not need any extra salt at all since olives, anchovies, and capers are all fairly salty. Set Green Olive Salsa Verde aside. You can make this up to a day in advance.
Cook salmon:
Heat oven to 375° F. Line a rimmed baking sheet with parchment paper (parchment paper is optional but it makes cleanup easier).
Place the salmon on the lined baking sheet, skin side down. Drizzle with about 1 tablespoon olive oil and rub over salmon to coat evenly. Season with kosher salt. Place on a rack in the middle of the oven and roast until fish is just barely cooked through. Depending on the thickness of the salmon, it may take anywhere from 12 to 15 minutes. If you prefer medium-rare salmon, start checking the salmon at 10 minutes.
Transfer the salmon to a serving platter or individual serving plates and top each piece with Green Olive Salsa Verde. Serve immediately, with any extra Green Olive Salsa Verde alongside.
Leftover salmon can be stored in an airtight container in the refrigerator for up to one day. Any Green Olive Salsa Verde that was unused can be stored in an airtight container in the refrigerator for up to three days.