Same Situation
I also got my card yesterday, and well just a as an educated guess, more important to give your employer a courtesy copy of your GC, you need to get a new copy of your Social Security Card with the restriction of "Authorized to work with USCIS authorization" line removed. That can even be done by mail. Other than that, that should be it.
If there is somebody out there who have actual facts of something else to be done, please post it.