There isn't much difference, but my first reaction was that I would definitely use "that" in the first example and "it" in the second. However, I can't think of any general rule I would be following by doing that - maybe it is because "meeting" is a noun and "cut my hand" is an action. http://koreamosaic.net/elp/extras/general/itthat.htm has some guidance on it/that - reading that, perhaps the reason is that "cut my hand" counts as an "interesting new fact" whereas the meeting is something that both people in the conversation knew about before, even if one of them had since forgotten about it.

I personally would say there is no difference in those sentences.

Thank you for answering me! I'll try to be careful about the difference between them.

To me, using "it" or "that" changes the sentence. You can't treat them as the same word.