Freeing up space · Free Up Space wizard and button
What does "Put the link back" mean on a half-finished move?
Short answer: It completes a move that left some files behind, in one click. Nothing was lost meanwhile. If macOS won't allow a link in that spot, Storage Studio says so rather than retrying.
It finishes a move that got most of the way but left some files behind. Nothing was lost in the meantime — the files that moved are on your fast drive and the rest are still on your Mac. One click on Put the link back completes the rest.
If a repair genuinely isn't possible — for example because macOS won't allow a link in that particular spot — Storage Studio tells you so instead of retrying pointlessly. In that case the files stay where they are and you can decide whether to move them back with Move back.