Depends what you mean by "organized folders".
If you already have "auto-organise media files" enabled, you can update the path setting and MusicBee will move your existing files. If you don't currently use this, be aware that it will organise all of your music so make sure you set up it correctly before enabling it.
Otherwise, you could select all the files for artists that start with "The" and use Send To > Folder(Move) > Move Files to Organised Folder with an appropriate path template to update only those on a one-off basis. It shouldn't take too long, and you can preview the paths to make sure they look correct before proceeding.
Bee excellent to each other...