I'm still here, I was hoping for someone else to post, so that this didn't become just the 2 of us.
"Captain, my name is Lord Inquisitor Marian of his holiness' Ordo Hereticus. I am here on urgent business. This is an off-the-books mission, nobody is to know who I am and what my mission is. For this reason, not even you will be made privy to the mission specifications. All that I will inform you is that this mission is of the utmost importance to the Ordo Hereticus, and that, if failed, many Human lives will be put in danger. You are to inform your men that my name is Lord Commissar Marian, sent to take command of the conscript Planet Defense Force." She then unbuttoned her blowse and revealed the glowing tattoo of the Inquisition seal on her stomach, just under her right breast. "If you require further authentication, please ask behind closed doors."
<Snipped quote by mattmanganon>
If she doesn't trust the captain, why did she just hand the note over to a random Space Marine on the steps of the cathedral without confirming his identity first? Her cover identity has now been compromised, rather than simply presenting herself as a Commissar until such time as she could gain a private audience to reveal herself properly.
The Inquisition holds no sway over the Adeptus Astartes, they they completely separate organisation who cooperate due to ancient pacts of support given at the time of the First Founding. A High Lord Inquisitor would have no additional authority to give orders to a Lamenter compared to a Lord Inquisitor.
The note is addressed to 'Commander at Hive City Acane', which would mean either the commander of the local PDF or the civilian governor, depending on the local hierarchy, but has no bearing on the Space Marines. She appears to be trying to use a specific order as a carte blanche to requisition any assistance she can, something which as a Lord Inquisitor she could do anyway.
Why would the Space Marines accept a note without any form of identification instead of a far more secure electro-tattoo? It's possible this piece of parchment is either a forgery or that it's been taken from the original owner. Verification of the document would be required before it could be of any use, and that would take time, communication with the office of High Lord Inquisitor Fyodor Karamazov and would increase tensions between Marian and the Marines which could've been avoided had she simply introduced herself as a Commissar.
If she'd just flashed her tattoo and said "Inquisition business" the Marine would've simply accepted her authority until such time as she proved a threat to the sanctity of the Chapter, with no further explanation of her actions required.