Synaptic remove "gedit" wants to remove "ubuntu-desktop". How can I reinstall "gedit"?

I want to make a clean start with gedit; ie. remove all customization.

Synaptic Package Manager, indicated that ubuntu-desktop would also be removed!

Well, that sounded to be a bit on the dramatic side, so I tested it in a VM..

It was dramatic!... I lost my Ubuntu Deskop! (...funny about that!)

Okay, my potential disaster was averted thanks to VMs, but I still want to fully uninstall and reinstall a fresh instance of gedit.

How can I do this?

You shouldn't lose your desktop by removing ubuntu-desktop, because it is a meta-package that simply allows to easily install all default packages in the Ubuntu Desktop environment. However, it is recommended to install it again before any system upgrades.

You can safely remove gedit and ubuntu-desktop, then install ubuntu-desktop again. It will automatically select gedit for installation, because gedit is included in the meta-package.

Although is perfectly safe to do what you want, is usually unnecessary to re-install applications, unless they got corrupted by a power outage or broken update. As @sagarchalise commented, deleting the config files for the application usually solve most problems and if you are looking to reset your customizations, then that is the way to go. Re-installing won't change any personal customization.

Note: after reading your message about losing your desktop, I did a test on a VM, just to make sure nothing has changed since Maverick. I didn't lose my desktop even after rebooting and I was able to install both packages again.

If you want to remove all customisation then reinstalling Gedit would not help at all. All of your Gedit settings are stored in your home directory with gconf so after reinstalling Gedit all of your settings would remain the same. To remove your settings you could remove the directory ~/.gconf/apps/gedit-2. You can find that folder by turning view hidden files on in the file browser.