When I drag a footnote from one place in the text to another, the original highlighted becomes highlighted again (green with underline indicating link to footnote) as soon as I type something. Although highlighted, however, the original word is not linked to the footnote.
Scrivener 3.1.5
MacOS Catalina 10.15.2
MacBook Pro (Retina, 13-inch, Mid 2014)
I suggest you try Project > Project Settings… > Format and at the top of the pane “Choose Footnote Marker”. The default is an asterisk but you can edit that if you wish. In future, choosing Inspector footnote puts your selected marker in the text, without highlighting any word(s), and it can be moved around without leaving any gremlins behind.
HTH
Mark