What reward did Holmes ask from the king? Why do you think he chose this particular reward?

Holmes requests the photograph he obtained from Irene Adler: the very same photograph that the king had hired Holmes to find. This is a peculiar request because Holmes does not show a lot of interest in women. I think he wants Irene Adler's photographed because she had outsmarted him. Holmes holds her cleverness in high esteem and wants to be reminded that he can indeed be outsmarted.