You can uninstall or removes an installed barnowl package itself from Ubuntu 16.04 LTS (Xenial Xerus) through the terminal,
$ sudo apt-get remove barnowl
If you would like to remove barnowl and it's dependent packages which are no longer needed from Ubuntu,
$ sudo apt-get remove --auto-remove barnowl
If you use with purge options to barnowl package all the configuration and dependent packages will be removed.
$ sudo apt-get purge barnowl
If you use purge options along with auto remove, will be removed everything regarding the package, It's really useful when you want to reinstall again.
$ sudo apt-get purge --auto-remove barnowl