Is there really anything he can say or do that will redeem his public image after he's been slandered on a global stage based on a internal-only memo that someone leaked to the public likely with the intent of ruining his life?
There is a point at which there is really nothing you can say to make a situation better, and you are better off just not saying anything further on the matter.
Autism does not cause you to be a bigot.
As a fellow member of the spectrum, I can fully see where Damore fits on it. In some ways I agree with his actual points (not what the media has claimed they are), but his presentation was poor, and insensitive to how it would be received. And a good chunk of his memo was just... not good. He never intended it to be public, and it certainly wasn't fit to be (I believe he considered it a work in progress, and was looking for constructive feedback), but someone angry at him decided to make him a public figure overnight by leaking it and ruined his career.
He obviously made some very poor choices on who to associate with afterwards, not realizing the political implications that came with them. He failed to see how free publicity provided by certain parties would associate him with them.