To iron someone's back

any input on this one

Never heard it here in my part of the U.S. I've heard of "watching someone's back" or "I've got your back."

Perhaps it is being used in the same way that somebody would speak about combing somebody's back. It is a sign of advancing years that we men try to become like alpha male gorillas - the silverback - and develop more hair growth on our backs. In some people hair growth is quite noticeable and so remarks about combing it are made. If it was particularly thick, one could offer to iron it flat.