It looks like the USB cable’s shield, am I right? If so, the basic idea is to prevent the USB cable from acting line an antenna, for two reasons: 1) so no radio interference can affect the USB signal and 2) so the USB signal doesn’t radiate and cause interference to other devices. It’s connected to the metal hood on the console side, and whether or not it should be connected on the other end is left to the designer*. Interference could mean connection problems, incorrect info sent, etc. In short, you’ll probably never see an issue from it being unsoldered, but it’s a good idea to solder it back down.
*A good, if a bit technical, discussion on this can be found at http://forum.allaboutcircuits.com/showthread.php?t=58811