You were lucky!
Not sure I understand the problem. You have a battery grip, and the grip has a lug for a hand strap, which attached to the top-right-side lug on the body, and the bottom-right lug on the underside of the grip, so the strap is on the right side of the camera. The L-bracket attaches to the tripod socket, and the vertical part is on the left side of the camera.
The Canon E2 Handstrap will work fine. Ok, now I see the problem...it's pictured with a tripod socket connector. But, it's not needed with a battery grip. The E1 required a battery grip or a 1-series body. Canon replaced it with the E2 that includes a tripod connection so it can work on any body. But since with the grip you have two lugs, just use the strap detached from the tripod socket connector.
Some L-brackets do include a strap lug - usually the ones designed for non-gripped bodies - with a grip, the lug on the L-bracket is superfluous.