Seeing an image of the actual control would help to determine the type of control and what's needed to modify it. In any case, the first thing you will have to do is stop the VI so that it is in edit mode. Hopefully, there is a stop button on the front panel. When you click that, does the main VI stay visible or does the whole thing disappear? If it stays visible, then you have to go to the block diagram (CTL+E) and find the subVI that is displaying this pull down menu. If you can find that and the control that you click on for the menu, see if you can right click on it and select 'Edit Items'. If this is a very simple menu control, you will have a list of items that you can edit and then save.
You should know, however, that there are many ways to populate a pull-down menu and the above procedure may not work. You may have to spend quite a bit of time learning a lot about LabVIEW or post the entire program here and let someone else look at it.