A somewhat late reply to a question that I asked myself recently.
The GR-E2 is functionally and electrically interchangeable with the GR-E1 grip. It differs from the E1 by enclosing the battery behind a door that offers better water protection.
Note that there are two versions of the GR-E1 grip. The first (and oldest) was released with the EOS 1 and is designed so the battery just slides into position. This is the grip that's illustrated in the EOS 1 user manual I have.
The second version of the GR-E1 has a grey plastic rotating piece that the battery slides into, which makes removing the battery a bit easier. It's the same mechanism that used on the BP-E1 battery pack. I'm not sure when the second version of the GR-E1 was released, but it's pictured in the EOS 1N user manual, and going by the pictures in the EOS 3 manual it appears to be the grip that it was supplied with.
The GR-E2 is pictured below, it was introduced with the EOS 1V. Note that a hinged door covers the battery space, and the grey plastic battery locating piece on the top is absent.
All three of these grips are interchangeable. eBay sellers usually don't differentiate between the E1 and E2 versions, all of these were listed as GR-E1 grips.