Wow the MC is pretty stupid or a least really unmotivated. TBH i don't think she's going to blackmail the teacher that bad as she probably won't think of how. I am guessing how she is going to blackmail her is just get her to teach her in cram school so that she can get her grades which isn't really blackmail because thats her job.
Either that or she’s going to use the blackmail to have the teacher meet with her for free, or to have the teacher adjust her grades. Which, knowing the MC, would still likely result in her accidentally learning something.
Wow! You just don't get how this MC thinks. She is FAR TOO LAZY to blackmail anyone! If she meets even a hint of resistance, or work, she just folds immediately.
I think this will be about making her a better person, who thinks about others.