I had a bit of trouble with the quest at first not knowing how I was supposed to start it but the item that you get from her is a hint of who to ask. As Leonora Rose said, if you try to give it to the wrong person it's no problem, they'll just refuse it and say it's not from them so you can ask the next person you think of. Once you get the connection between the item you get and who you're supposed to give it to, it becomes a fun, simple quest.