The manual says to slide a thin coin in between the two halves where the key ring is, then twist it to pop open the halves. Don't remove the rubber, and don't wipe off any grease inside. If you don't have TFM to R, you can get a PDF copy from the Tech Section, which is linked at the top of this forum.
FWIW, Lincoln officially says that a weak battery will not affect the range of the transmitter. My experience mirror's Todd's, that a weak battery does decrease range. There's a TSB on the "short range" issue, but I haven't looked at it in quite some time. My remote seems to work from as far away as 50 feet, depending on obstructions. I haven't tested it to see what the max distance is.
One guy I know used to get better range by holding the remote to the underside of his chin when operating it. I once got a really long range operation (well in excess of 50ft) on my SHO's remote by holding it against the metal pole for one of the parking lot signs--but only once. It never did that again.