“Authors Response” or “Authors’ Response”?
I really doesn't matter: all of these are close enough to one another to be clearly sensible and have plausible arguments for why they might be reasonable. More importantly, none of them will make it into the published paper: they are merely a transient piece of communication between you and the editor and reviewers which will later be deleted.  As such, any of them is reasonable enough.

That said, personally, I would just say "Response to Reviews" and avoid the whole question.