Einstein never claimed that Gravity did not exist, but rather that since Gravity seemed to affect objects instantaneously (eg. faster than the speed of light), then it could not be functioning as a force in his model of GR (since nothing can travel faster than the speed of light according to GR). Einstein also stated that the effects of constant acceleration were indistinguishable from the effects of gravity (equivalence principle).
Check me if I'm wrong, but Einstein predicted that gravity propagates at the speed of light (experimental evidence later supported this prediction). Newton was the one who said that gravity was instant.
I believe that you are correct in that he eventually arrived at that conclusion, however, when he was first postulating his ideas on GR (which is around the time when he started treating gravity as a warping of space/time) I think he was going off of Newton's assumption that it was instantaneous.
However, we are now arguing semantics (to some degree) at this point. The assertion was made that Gravity does not exist in a RE model, and there are 63 pages on the sticky forum alone regarding Gravity that challenges and argues this point of view.
Einstein never disproved gravity, he never said that it did not exist, he just chose to look at it a little differently than as a force to help explain mathematically why the orbit of Mercury around the sun was significantly different than the orbits of other planets around the sun (it broke some of Newton's formulas).
Einstein was creating a more accurate model of the universe and how it behaved than Newton, but for all practical purposes, on the face of the planet, Newton was extremely accurate. Today, quantum physics shows that Einstein's equations were not completely accurate at the quantum level.
But I digress, Gravity itself has not been dis-proven from a RE perspective and it is erroneous to say so. The only thing that has changed is how Gravity is viewed.