That's quite certain to taint any results they might obtain and form into a case for a Tribunal, and to open it up for the counter-case of the High Crime of 'meddling with mundanes'. It is also likely to endanger them and even the Order, if the prior mentions his sodales to church investigators - who will question him thoroughly if they find evidence for him being a necromancer or worse.
Can't magi in the cathedral chapter just push for an independent - but well briefed - Quaesitorial investigation of the prior of Wenlock instead? After all, the Quaesitores can also proceed to march him on the spot before he rats to the church.
In that case the role of Lord Henry would also get much easier. He could become just the concerned widower he likely is, caring for body, tomb and masses of his late wife: attending some liturgies of the monks, supervising the repair and embellishment of the tomb, enquiring about the missing skull - and often bringing close friends from the cathedral chapter with him to share his grief and provide some solace. In this way the chapter assumes the role befitting local magi in this mess, namely as observers and force in the background, while the investigative work is assigned more efficiently as well.
Calling for the involvement of Cluny could be left to Lord Henry then, if eventually something worthy of ecclesiastical attention comes up, whose investigation does not risk to compromise the Order of Hermes.