Q: removing software

Do you mean the administration software ARD Admin? As detailed here:

http://www.apple.com/uk/remotedesktop/

and here:

About Remote Desktop Admin 3.8 - Apple Support

Or do you mean what you see mentioned in software update? As detailed here:

About Apple Remote Desktop Client 3.8.4 - Apple Support

If you mean the former then simply delete the app as it is a download from the App Store. If it is the latter then you can't remove the 'Client' as it is part of the OS. You can choose to not update it, if you wish, you have that choice with any update. Apple Remote Desktop Client is not enabled by default. To enable it activate the setting in the Sharing Preferences Pane called Remote Management. If your computer is only used by you then there is no real need for you to consider, enable or worry about it. There will be many elements/aspects of your computer and the OS you won't be aware of, use, or even need. This is entirely normal and should be no cause for concern.

Hope this helps?