Madeleine Perridge, Head of Antiquities at Bonhams, has emailed that the auction house is investigating the new cases denounced by R. Pintaudi with the relevant authorities. Whatever the outcome of this investigation will be, the episode demonstrates that a direct and closer collaboration between academics excavating in areas where looting and illegal excavations are occurring and auction houses and dealers is absolutely necessary in order to curb the illicit trafficking of antiquities. This implies first and foremost to find ways to improve current practices in checking provenance documents, as I suggested in my previous post.
Roberta Mazza 
Did she say whether they will be contacting the client who bought the piece from them, and if so, at what stage?
The email does not go in such details; I imagine there must be some official procedure that the auction house and relevant authorities will follow.