The backing is usually cheap, but keep in mind that the whole iPhone will need to be disassembled for it to be replaced. It is not necessarily an easy process and would require a cool mind and steady hand. If you find a third party repair centre to do the work for you it will be more in the price range of $60-90 for it to be installed.
Most of the replacement backings available are chinese knock-offs which work but may not have the exact standards for the Apple manufacturing plant. The re-assembly will also require some glue to attach the metal band onto the backing, so it will take some time as you need to wait for the glue to dry. I've replaced two backs on two different iPhone 3G's. One turned out great, and the other one not so much as the backing was off a bit giving some sharp edges around the metal band.
If it is just scratches then maybe just get a case to cover it up. Just a thought.