Harry didn’t pay much attention to the testimony after the beginning, thus the timeline doesn’t have to change if he goes back to make sure it contains some new False Memoried tidbits, if he can get someone to do the charm. But I don’t think there’s been much indication that he can override his Time Turner limitations by himself and there may be little time left to try and get someone to do it for him before Hermione is hauled off.
Edit: Silly me, he could just decide what to make her say later and do a quick check from McGonagall if they were included (thus checking if he will manage to go back to do the deed) and go from there. But it’d be difficult to insert subtle enough bits to make a difference only when lampshaded by Harry afterward (since many others presumably listened to the whole testimony already without noticing). Not impossible though. [Re-edited for semi-clarity...]
I thought you couldn’t change the past with a Time-turner.
Harry didn’t pay much attention to the testimony after the beginning, thus the timeline doesn’t have to change if he goes back to make sure it contains some new False Memoried tidbits, if he can get someone to do the charm. But I don’t think there’s been much indication that he can override his Time Turner limitations by himself and there may be little time left to try and get someone to do it for him before Hermione is hauled off.
Edit: Silly me, he could just decide what to make her say later and do a quick check from McGonagall if they were included (thus checking if he will manage to go back to do the deed) and go from there. But it’d be difficult to insert subtle enough bits to make a difference only when lampshaded by Harry afterward (since many others presumably listened to the whole testimony already without noticing). Not impossible though. [Re-edited for semi-clarity...]
He could alter Hermione’s testimony in a way that’s contradicted by new evidence that hasn’t yet been presented.