Smash the garlic, sprinkle it with salt, and mash and smear it to a paste using the flat side of a knife. Add the garlic paste to a medium bowl along with the anchovy, vinegar, pepper flakes and some salt. Whisk to combine, then slowly whisk in the olive oil until emulsified. Add the tomatoes, olives, capers and chopped basil and gently stir to combine. Let the relish sit at room temperature for at least 15 minutes to allow flavors to meld.
Heat a grill to high. Rub both sides of each swordfish steak with two of the basil leaves, leaving some of the now-bruised basil on top of each steak. Brush the steaks with the canola oil and sprinkle with salt and pepper. Grill, basil-side down, until charred, about 4 minutes. Turn and cook until opaque throughout, another 4 minutes. Remove to a platter and immediately spoon the relish over the fish.