Is this really a problem?
Mary Sues in fictions, especially fan fiction, are annoying partially because the world warps to suit them. In an RPG that will not happen (or at least not in the same way) because the other players and the GM provide elements that are out of the hands the person running "Mary Sue". Mary Sues also tend to be too perfect in ways that are reflected in the mechanics (good at everything, or the youngest something ever), but this also doesn't come up in an RPG because the system limits the character.
If you mean the character is being played as overly friendly, tries too hard to be likable, and has no character flaws, that might not be too much of a problem. Some people at least try to be like that in real life. The archetypal paladin is highly charismatic, strives for justice, and is a natural leader. And if the fantasy the player wants to play out is a character that is almost immune to temptation and too perfect then it might not be a bad thing to let her, especially if it fits the character concept.
As others have mentioned, one way to help make the character is to start placing her in positions where she has to make hard choices. Give in to temptation to advance her own power, or take the high road? Save the child, or the village’s one and only healer/doctor that the whole village will worry about? Hard questions help define and solidify the character. Mary Sues in fan fiction either tend to not face a hard choice or they come up with some miraculous way to satisfy everyone, but in an RPG with constraints they can't do that and need to make the choice.
Talking to her Out of Character
I partially agree and partially respectfully disagree with KRyan on this. I would certainly talk to her before trying to do anything drastic to her character, but that isn't necessary if your approach is to present the character with hard choices and isn't even necessary to do things like have NPCs react to her realistically, but in a way that shows how the character can be annoying to them too. It’s then her choice to alter the way she plays or not.
In Go, some teaching games are played with very few words uttered. Instead, the teacher plays in such a way that it highlights how the novice can improve. This is often a much better way since it encourages the student to figure it out and they tend to learn the lesson more deeply that way. Now, of course RPGs are different. In Go it is possible to objectively say that one play is better than another and that is hard (impossible?) in an RPG. But the concept is similar. Highlight in character the consequences of certain things through NPCs, and present opportunities that will help develop the character.
Talk to the Group
If you single her out, even if you do it when no one else is around, it’s hard not to make her feel singled out. But you can approach the group as a whole and just make a general statement that you want to improve the roleplaying and can hand out articles about doing it well to everyone. Also, you can praise others for doing the things right that you think she could improve on. Some people take criticism well, some don't. But praise is easier to do right. And you can also have a vote for best roleplayer for a session, so the praise is coming from the entire group, not just you. But they have to explain why that person is the best for the session and that will naturally highlight the things everyone else can do better.