Cut the eggs in half lengthwise and carefully scoop the yolks out and into a medium mixing bowl. Mash the yolks well with a fork.
To the bowl, add the Greek yogurt, Dijon, relish, salt, and pepper. Stir well to combine, making sure the mixture is smooth and creamy.
Use a spoon or piping bag to divide the yolk mixture between the egg white halves (about 1½ teaspoons in each). Sprinkle with paprika if desired and serve.