The card appears to be random compared to the 3-pack. When you open the 3-pack it displays a small menu and asks you to select the icon of the girl you want the pack to apply to. The single card does not give you this option. Both free weekly cards I've had went to two girls I had not been accessing.
I have noticed the card seems to be restricted to girls that are currently unlocked. You could try to control who gets the card that way, but only Cherry would have an absolute guarantee.
I think if there was an option to choose which girl gets the card, then it would be really simple on how to do it.