How did they dispose old Joe's wife's body in the movie Looper (2012)?

I don't believe they did dispose of her body.
The reason for loopers is mainly so organised crime lords can make people disappear. Hard to argue that so and so was killed when you can't track a body.
Joe's wife was what might be considered collateral damage. They most likely wouldn't get any blow back from anyone other than Joe so no need to dispose of her body.

Also, the Rainmaker was closing loops wholesale so he may have found other ways of disposing of bodies. The loops where closing over a matter of weeks for young Joe, but this may have been mere days for the Rainmaker in the future.

If I had to pick one answer though, I'd say she just wasn't important enough to have to disappear, dead was good enough.