I agree... either 'that" or "which" or nothing at all can be used here. It's just the preference of the asker. but, if you ask this way: "Do you know that/which new movie they are talking about?" in this case, "that" describes just one 'new movie' in particular, while "which" to a multiple titles of 'new movies'. :)

you can say "that", "which" or nothing at all. Most common way of saying it would be do you know the new movie they are talking about? Any of the three options is correct.