Edward, according to this site, the bayonets were affixed to the rifles and muskets before they were stacked at Appomattox. It is entirely possible a particular bayonet was kept by its owner, especially if he had lost his rifle. Some battle flags were held back by the Confederates, in their reverence for them, with the full knowledge and consent of the union troops at the surrender.
As we embark upon noting the beginnings of the war, it is fitting to read Gordon upon the feelings of both Conqueror and Vanquished at it's end. He even has kind words for Sherman, in his offering of good terms to Johnston's men, to the point of allowing them to keep their firearms, to be turned in at State Arsenals. Of course, his terms were rejected by Washington, but he did try to be magnanimous.
Reading Gordon's words will add to our appreciation of what the men who fought the war felt about each other, and what Booth caused in his misguided assassination of Lincoln, who had, whatever we otherwise might think of him, had asked Grant to "Let 'em up easy." Stan