He was, he supposes, hoping to keep the focus on them, rather than himself, but there's no reason to keep the details from them.

"When I took the sword back to Lan Wangji, I brought along some of the glass that was also there, in case he might learn something from that. I tried to bundle this up in our shirts--" Well, what was left of his own tunic, plus Magnus' hoodie. "I must have sliced it then. There were a few other very small cuts, but they are of no concern."