What's a "partially constructed" deviled egg?
Sounds like it's peeled hard-boiled eggs, sliced in two with the yolks removed to a separate bowl (or bowls) with some mayonnaise/mustard on the side... or maybe it's just peeled hard-boiled eggs?
Basically I bet the person who brought this 'dish' thought of a nice way to say "Here, I boiled me up a bunch of eggs and didn't want to do the work so I gave them a high-falutin' title". (You know, it is soooooooooo hard to mash up those yolks and add those hard-to-find deviled egg ingredients

agnes!