I have found from my own personal experience with researching company H of Cobb's Legion Cavalry Battalion (GA), the men still present for duty with the Legion cavalry in April of 1865 who were surrendered in NC and had their names listed on the NC surrender muster rolls (which I’ve seen), the following is shown on one of the cards in their compiled service record:

Appears on a Muster Roll of Officers and Men paroled in accordance with the terms of a Military Convention entered into on the 26th day of April, 1865, between General Joseph E. Johnston, Commanding Confederate Army, and General W. T. Sherman, Commanding United States Army in North Carolina. Roll dated Greensboro, N.C., April 30, 1865. Paroled at Greensboro, N.C., May 1, 1865.

None of these men have a copy of their actual parole papers in their compiled service records, but at least one man in company H who was not present with the Legion cavalry for the NC surrender and parole, but was later surrendered and paroled in Thomasville, GA, does have a copy of his parole paper in his compiled service record. I'm not sure what would be found in the compiled service records of men from other states who were part of the ANV surrender and parole in VA.