OP I just want to say that you sound like a fabulous employer and your nanny is just lucky to work for such a caring and considerate family!!
Anyway, as long as this doesn't happen too often, just chalk it up to a misunderstanding. Really it is no big deal.
You do not have to offer your nanny a gift card...it may embarrass her.
What my employers tend to do over stuff like this is simply add it to my pay. For instance, say your nanny makes $15/Hr and she worked an extra 15-20 min. for one day. I would just add either and extra $5 to her pay for that week or if you really feel bad, just pay her another $15. FYI: Us nannies LOVE it when as family rounds up.