Jeannie, you're not going to like this but my understanding is that once a debt has been turned over to a collection agency there is a contract stipulating the ageny gets a percentage of the debt collected plus expenses. I understand what you are saying but your timing was just off enough and once the collection agancy was authorized they need to be paid.
My advise is to settle with the collection agency and resolve not to be in this situation again. You will not win this and the cost will increase as you delay payment.
PS; I am not in the debt collection business and my advice is based on the experience I had being involved with one of my kids in a similar situatioin.