Xero,
I just got a call from my recruiters yesterday and they asked me for this. They wanted it to be a formal letter and not one sentance long either. I wrote up a couple of paragraphs and sent it off. Something to the effect of, "this is why i am reapplying."
also, if you write up a letter and give it to them, its not like they will complain that its not the "scrap" they asked for. can't hurt, so why even bother asking?