You completed the quest already when you opened the secret passage way, and I'm assuming you got the XP for it. You cannot complete it again.
sbgimp wrote:So when I first found the rangers in the south of elderoak forest, they never gave me the 'meaning of the note' quest.
A couple of people have reported the same thing, but neither of them could produce a save or were sure of the exact circumstances, so it's possible the passage was already open, or that you didn't follow the exact dialogue line; you need to follow a specific dialogue line, asking about the Nadaria first, before you can ask for the note.
The quest for the sister is not related to this quest, the sister only 'tests' you first before willing to give you instructions for how to enter Old Moonrise.
There's at least one thing that's a little bug, because Ranimer shouldn't offer the note anymore at all when the passage is already open, but he apparently does that when you've saved the tree and he hadn't given it before. That's one thing the developer should look at.
Of course, there's no way you could open the gate if you hadn't seen the note, because you would have no clue about the password, it could be any word in the dictionary, so the problem only arises when you have knowledge from a previous play-through or you got the answer from someone else...