I have an historical concern with expressing what these soldiers went through, as described in the primary source materials they left behind. Some of it is honorable, some of it isn't. I am not particularly concerned with the "impressions" that may result, just rigorous historical truth.
I have many first person accounts - diaries and letters - of this happening, mostly in the fall of 1861. As I said, some accounts were by men who found the practice repulsive, some by men who were sending items to a female friend. Like any other collection of men that were ever gathered, some of them were nice, and some weren't.
During this time, Gen Lee didn't command the ANV, but was being routed out of Western Virginia by none other than George McClellan.
As the war progressed, there was far less mention of actually disturbing remains, though soldiers continued to pick all sorts of items off the battlefields - pocket watches, walking canes, bucktail hats, haversacks, blankets, and of course food, shoes and clothes.