I'm guessing something was broken/excluded with the cleanup call for it. It remains onscreen permanently until you restart the client. The only thing I've seen successfully hide it is a screenshot(it even displays when you press escape to bring up your menu and will even haunt you all the way to the account login screen).
To add to this, I also noticed that when going to edit your UI layout, I actually saw two windows for the Singularity Meter. Was unable to take a screenshot of the double Meter, but did take one of the Meter persisting onto the Tailor UI:
I'm not sure if it was part of the cause, but I first noticed the strange meter behavior after the 2nd portion of Best Defense. I was auto-loaded into my shuttle, and my meter appeared to have shifted from its original location on its own. I didn't really pay it any mind until I went to warp out of the area and saw that the meter remained on the loading screen.
I can also confirm that restarting the client remedies the issue.