Well, not quite childish. But maybe silly.  I have to confess that I think that posting signs like this on a door is often silly.  But many others obviously disagree with my view, because they post such signs.  And that's absolutely fine.  
But even if it were silly, why is a Pope not allowed to be silly on occasion?  People who take themselves so very seriously are tiresome and definitely not good leaders.  I imagine that it is either an in-joke, or simply a way that Francis is showing the particular psychologist who gave the gift that Francis appreciates it.  
I think that what is much more silly than the sign is the attention that it has been given and the vehement negative reaction on the part of some.