Heat a charcoal or gas grill. If using charcoal, make sure you have a full layer of hot coals on the grate.
In the bowl of an electric mixer fitted with the paddle attachment, combine the butter, garlic, dill, lemon zest, lemon juice, 3/4 teaspoon kosher salt and 1/4 teaspoon pepper.
Place the oysters (oyster-side up!) on a platter. With two small spoons, place a small dollop (about 1 teaspoon) of the herbed butter on each oyster. Place lightly crinkled sheets of aluminum foil loosely on the grill grates. Place the oysters on the foil, making sure they're level so the butter doesn't spill out. (The foil keeps the oyster shells from tipping over.) Cover the grill with the lid, making sure the vents are open, and cook for 2 to 3 minutes, until the butter comes to a simmer and the oysters are just heated through. Sprinkle with sea salt and serve hot.