You'd need to download the gallery's 'config.xml' file and the 'images' folder (e.g. using a FTP program such as Filezilla) and then open the gallery locally in JuiceboxBuilder following the instructions here.

Just make sure that the 'config.xml' file and 'images' folder are together in the same folder when you open the gallery (the structure of the gallery may be different on your web server but the standard structure is required to open a gallery in JuiceboxBuilder).

You would not need to download the 'jbcore' folder or the gallery's 'index.html' page. JuiceboxBuilder will reinstate them when saving the opened gallery.
Also, you would not need to download the 'thumbs' folder. You can have JuiceboxBuilder recreate the thumbnails by deselecting and then reselecting the 'Resize Images' checkbox on the 'Images' tab.

I hope this helps (at least to clarify things).