The major had already informed Nero of the story they were going to go with. Charles and Henry had not attacked Nero, but had worked with him against an unknown traitor, and died in the line of duty. That would be the official story, and beyond that he was not allowed to share any other details with anyone for the time being.
He'd also handed over all the cards he'd collected from the three corpses, not that he had any use for them. If he were not a recruit, and had free time, he could have gone and sold the cards to a reclamation shop. They were completely qualified to take in random cards people bought, and Nero was sure that if trap cards were an issue they would have ways of identifying them.
