Alexei's shirt was left on him simply because it was obvious the he was carrying no jewels once they got his pants off. The shirt remaining on him is mentioned in one of the accounts (not Yurovsky) of the murders and subsequent Keystone Cops routine of the burial, burning, acid, etc. The reference specifically is elsewhere in the Forum, do a search, I posted it several years back when the fragment was first found. I'm not at home right now, so I don't have the cite, but I remember it is from one of the other accounts in "Last Act of a Tragedy".