How do I remove hidden backup files?

If you also have unwanted backup files in subfolders, it gets a bit more difficult:

find . -type f -name '*~' -delete

You can simply run rm *~ if you're sure there is no other file that you need which ends in ~

If it is gedit that is creating the backup files, you can open gedit and select Edit->Preferences->Editor and uncheck the option "Create a backup copy of files before saving"

And for nano, look in /etc/nanorc for:

## Backup files to filename~.
set backup  

and change that to

## Backup files to filename~.
# set backup