When deleting a reference variable, any resolve node pins using it will have a picker added, which won't have anything listed in their dropdown.
This isn't consistent with what happens if the user just breaks the link, which simply reverts the pin to a wildcard.
Refreshing the node fixes the issue.
The empty resolve node pin will have a picker added that won't be populated.
Refreshing the node will remove the picker.
There's no existing public thread on this issue, so head over toAnswerHub just mention UE-69895 in the post.