Could you just tell her, "I know you were just trying to be helpful, but I put that project aside for a reason. I'd rather you not finish my work without asking me, thank you!" Because once you've had that conversation, any further "help"/subtle attempt to undermine you, would be blatant rather than passive, and then you could bring it up with your supervisor. And if she's indeed trying to help, she'll have to back off.
In my job, it is not cool to touch someone else's work (and this general possessiveness is something I'm struggling with as I head into maternity leave, because I don't like handing off my projects! and until I start saying "I can't do it" my boss wouldn't dream of asking my coworkers to take over), but I know these things vary depending on the type of work being done, etc. It's one thing for a teammate to wipe a countertop for you or something like that, another thing to take a project from you that would get you recognition and appreciation from your boss.
Another option would be to say "You know what would be helpful to me? Please do X (boring, crappy, assignment you don't want). Thanks! I appreciate your help so much!" That would teach her.
