What am I obligated to do?

You may feel obligated to do more, but if you go and pick a nice card and send it that is all you need to do. Staying in touch is nice, and it says a lot for you that they still think of you even in times like this. You must have been a very good sitter, and be considered a friend. Write a note in the card don't just sign it, and they will appreciate it just as much. Oh yes a proper note is written in plain paper cut to fit the size of the card. This is so the family may remove it for the senders privacy.