I think what they were telling you when they said "transom" is the transom assembly, more commonly called a gimble. There are two pieces back there, the drive and the gimble. The gimble is the piece that holds and swivels the drive. The parts, working from the outdrive back are the helmet, gimbal ring and transom mount. there's a piece between the transom mount and the outdrive that runs through the gimbal ring and under the helmet that seals the u-joints. It's the boot. These deteriorate and should be regularly replaced.

It's somewhat rare for the gasket on the transom assembly to go bad. It wouldn't hurt to look inside the transom for signs of leakage though.

While you're there and have the drives off, the gimble bearings need to be looked at. There are four on each. Two for the up/down motion and two for it to swivel left and right. These are under immense load when running and they can wear.

Take a look here- you can see exploded views of everything inside the drives- http://www.mercruiserparts.com/selec...?doc_nbr=13668 Yours are the SSM III (old style)