On more than one occasion i've ended up having to unwrap gifts in order to clear a bag. It's usually when someone is bringing leaden crystal as a gift or in one situation a set of butcher knifes. So yeah, in general wrap gifts after you get where your going. Lol, I remember last year a passenger put a big wrapped gift through the machine that I had to re-run because the image was cut off. I didn't have to check the bag but a little kid asked me if I could see what was in the box and if I could tell him what it was. I guess he couldn't wait until christmas.