You can uninstall or removes an installed libunity-gtk2-parser0 package itself from Ubuntu 14.04 LTS (Trusty Tahr) through the terminal,
$ sudo apt-get remove libunity-gtk2-parser0
If you would like to remove libunity-gtk2-parser0 and it's dependent packages which are no longer needed from Ubuntu,
$ sudo apt-get remove --auto-remove libunity-gtk2-parser0
If you use with purge options to libunity-gtk2-parser0 package all the configuration and dependent packages will be removed.
$ sudo apt-get purge libunity-gtk2-parser0
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 libunity-gtk2-parser0