Not quite an in Dome thing but I was watching clips of Conan and noticed that there was a Flames retro Home jersey hanging in the hallway.
Did some research and found out it was this:
Through one of his skits over the years Conan came up with a super hero character he called "The Flaming C". The Flames getting wind of this sent him a framed jersey letting him know about their "Flaming C".
On the back it's crested as "O'Brien" with the number 11, for 2011 when they sent it.