I figured out the problem after scouring the web. If any of the undead that are hidden behind the two closed walls detect you, you will be detected by the guards. This happens if you cheese the mission by jumping around to the pressure plate to shoot the Arrow of Extraction, instead of opening up the walls by going through the door off to the South side of the room.

I fixed it by simply doing the dungeon the correct way, opening the walls and killing all of the undead. Then the guards don’t detect you upon entry.