In a small bowl combine the vegan mayo, ketchup, mustard, relish, ½ teaspoon garlic powder, ½ teaspoon salt, ½ teaspoon smoked paprika, and the pepper. Put it in the refrigerator to chill until the burgers are ready.
Add the beans to a bowl and mash with a fork or use a food processor to break down the beans. If using a food processor, transfer the mashed beans to a bowl.