Slice the hard-cooked and peeled eggs in half lengthwise. Use a sharp knife, but not a serrated knife because it will leave marks on the egg white. Pop the yellow yolks into a small bowl and mash with a fork. Add in the mustard, Durkee's, Wickles relish, and mayo and stir well until the filling is completely combined.
Scoop the filling into a plastic sandwich bag. Fill the eggs or store in the refrigerator until ready to fill.
When you are ready to fill the eggs: Line the egg whites up on a desired serving platter. Snip off the corner of the sandwich bag, so that there is a ½ inch opening, then gently squeeze filling into the egg whites.