and was only a problem if you used their software to run your backup solution with.
As you are using Time Machine, which does not use any of the software that comes on the drive, you will have no problem at all.
Personally, I used Disk Utility to format the Western Digital drive as OS X Extended (Journaled) which destroys any of the factory installed software and leaves you with a clean, empty, drive
Now go update to Mavericks, assuming your machine has the required specifications
P
I need some help here. Do I or do I not upgrade to Maverick? Since I use a Western Digital back up drive is it safe? I read things about the software that was provided by Western, but I have always used Time Machine to activate the back up. What is this software from Western that is so apparently dangerous? How do I identify it and if necessary remove it? Once removed can i back up to Maverick without further concern, or is this still a subject as yet to be resolved.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic