Spoon the dill pickle relish into a fine mesh strainer set over a small bowl and press it with the back of a spoon for about thirty seconds to release the excess brine. Pat the drained relish dry with a paper towel, then drain the capers the same way.

Chop the capers and mince the fresh dill. You want the capers about the size of a lentil, and the dill chopped fine enough that it disappears into the sauce instead of sitting on top in long strands.

Whisk the vegan mayonnaise, lemon juice, Dijon mustard, onion powder, salt, and black pepper in a medium bowl until the mixture is smooth and glossy.

Fold in the drained relish, chopped capers, and dill with a spatula. Stop as soon as everything is evenly mixed, because overworking a vegan mayonnaise-based sauce can make it look grainy.

Taste the sauce and adjust it. Add more lemon juice for brightness, more salt if it tastes flat, or a small pinch of sugar if your relish is sharply sour. If it's thicker than you'd like, whisk in water a teaspoon at a time.

Cover the bowl and refrigerate for at least thirty minutes, or up to a day, so the flavors can meld. Give it a stir once before serving.