You need to declare the bow and arrows as such at the time you check the bags. I have had bows scratched by TSA inspections in the past, where they have jammed the bows and other things back in the case without worrying about things like getting things back in the right slots. In that sense, I think the 3 Rivers tubular case is a better idea than the flat cases with foam cutouts, because TSA doesn't try to get things back in the cutouts. I have heard that people can sometimes get the TSA inspection done right there while they are watching, which would be great if you can get them to do that.