While I was up on the lift today, I noticed that the shiny metallic circle thing attached to the back of the diffy doesn't seem to be attached to anything else. Just bolted on... I can't seem to find any posts about what this might be and it's function.

 

It's a vibration damper.
Although most (all?) XF diffs have had the mounting holes from the get go JLR only started fitting them from around 2013 I think.

 

thank you! it was really bugging me. I will leave it be in that case...