It pretty much just helps to muffle the sound of the air intake. Either removing some of the raspy sound to it or reducing the volume of the sound in general.
In this pic, I'm not sure if you're (or they're) referring to #14 or #13.
http://www.hondaautomotiveparts.com/...y5=AIR+CLEANER
If it's #14, then tell them to forget about it, and just plug the hole in the air flow tube when the vehicle is returned to you. If it's #13 (the "Muffler"), then it might be an issue of not having anything to connect the air flow tube to the air cleaner box. It appears to have an oval shape on the air cleaner box, verse a round shape of the air flow tube.
If it's neither of those parts, and is attached to the bottom of the air box (past part #12), then it might help against sucking up water into the air box as well.
But any way, you could always go to a local car parts lot, and probably find the part there, for a few dollars, rather than spending that much for a brand new part.