A pic would be nice. But as said above why are there 2 wall back to back without a top? That is just crazy. I been in the bricklayer for 15 years and have seen crazy stuff but this one is new to me.
Are the 2 separate walls just a single brick meaning 4 inches deep.? That is in it's own right wrong and not very structural. The way I see it there are 3 options.
1. If the walls are at least 8 inches thick a peice tear one down, that would make a big mess and is probably not something you want to do. Maybe one of the walls is on someone else property hard to tell with seeing it. Even so you could tear on wall down and still have the other. But the back side of the other wall is most like not finished (we call it striking when finishing a wall) so that would be an ugly wall to look at.
2. Do what the others have said and try to kill it by cutting it down as far as possible and smothering and whatever to kill the tree. That way, as also stated, is a hope for the best kind of thing. You know it will happen again.
3. Without seeing it, and what I believe would be the best option would be to do option 2 cut it back do what you can to hinder more growth than cap the walls with some kind of masonry. I'm sure you could find a bricklayer that would be happy to do it for you, or you could try it yourself. You can get 20 in. wall stones that would give you an inch projection on either side. That would look very good in my opinion that is what should have been done in the first place. Of course that will cost money. There are many options for capping the wall, it could get costly, come of the custom caps are not cheap but you can find something that might suit your taste that might not be super expensive.
If you lived closer I would be more than happy to do something like this for you and it would be bad ass.
Any other ?,s and I will be happy to answer them for you, good luck.