I haven't used my Canon EOS 630 for a while. The hand grip is sticky. I tried cleaning it with Lysol 4 in1 household cleaner,which didn't work. The camera is in great shape.
The sticky "handle" (most commonly on palm door on mid-range to high end EOS bodies) is a long-standing gripe. It is terrible when handling the camera with gloved paws, worse still if the surface comes into contact with something like Polartec fabric where it tends to attract pill which is very difficult to remove. I have treated my palm door (handgrip is not affected) on my EOS 1N with methylated spirit, which works for a while before the situation reverts again! From around 1992 to 1997 Canon offered replacement of the "sticky palm door" with another (at owner expense!) due to this manufacturing glitch. Some cameras, like yours, have the even more infuriating sticky handgrips. Don't apply solvents as they can potentially cause bubbling of the underlying surface. Try soapy water and also shampoo lather.
I'd just get a new grip, if the stickiness is on the removable part. There's three available for the 630: the GR-30 is the standard grip, the GR-20 has a remote socket, and the GR-10 has a slightly longer grip that can accept a hand strap. The GR-10 is very nice when using larger lenses, I have it on all three of my RTs. Nobody wants these cameras anymore, so I imagine the grips can be had cheap.