In context, there is no difference. Both mean exactly the same thing!
But in other contexts, there can be a major difference in /agency/.
That man killed my mother!
That man killed my mother for me!
In the first case, we would not assume that the speaker wanted their mother killed. In the second, we would.
So, they are different, in general.
But it is uncommon to have a case in which Kate did my homework for me without my intending that she did so - so we assume that the teacher did not have those cases in mind. So the meaning of the two ends up the same.