I simply leave mine as-is, @ryan91. Sometimes, when their "season" begins again, they will re-bloom. But often they will not and that stem will simply drop away. I am not sure there is an advantage when removing them or leaving them. I am sort of a "let-nature-do-its-thing" guy.
By the way, welcome to NGA/ATP.
drdawg (Dr. Kenneth Ramsey)
The reason it's so hard to lose weight when you get up in age is because your body and your fat have become good friends.