Prompt When Ejecting Time Machine Drive

Solution 1:

Could it be that there is a hidden partition available on that drive?

Disk Utility can show hidden partitions, but be default it doesn't do this. You can enable this feature by first enabling the program's "Debug" menu. Just enter the following command in the Terminal, which will edit the Disk Utility preferences file accordingly:

defaults write com.apple.DiskUtility DUDebugMenuEnabled 1

Now relaunch Disk Utility and you should be able to see the hidden partitions by choosing "Show Every Partition" from the now-present "Debug" menu. Do keep in mind that editing hidden partitions may not be a good idea in most situations.

Solution 2:

So, I followed @bart-koopman's advice and enabled Disk Utility's Debug menu. There are definitely more than ONE partition on my external drive. Here's what it looks like:

Notice that only "My Passport" is mounted at this point. I was about to give up, when Time Machine did its thing and completed a backup session. This is how it looks like now:

I have no idea when the "Boot OS X" partition was created. But I am pretty sure this is the extra hidden partition that caused Finder to complain every time I eject the drive. It gets mounted after a Time Machine backup session and stays mounted the entire time.

Mystery solved?