If you've moved a structure and the backtie hasn't moved with it, it's likely your backtie had a fixed position, meaning the backtie has remained at the specific coordinates set for it.
If the structure has moved a significant distance, there may be no valid backtie styles available, and the warning shown below will be visible in the 'Edit Backtie' dialog.
There are two methods of fixing this issue. The first is to delete and re-add your backtie(s).
Alternatively you can edit the position of the existing backtie(s), either by manually entering new co-ordinates or changing to a 'Dynamic position' which will place your backtie a defined distance along track from your structure.
Whenever you go to move a structure using either the 'Move' or 'Multi-move' functions, if the structure has a backtie with a fixed position, a warning will appear as shown below.
More info: See Adding a Backtie.