A Delicate Matter is a side case in The Sinking City. It is a side quest given by Robert Throgmorton.
He asks you to go check on Herbert Glover, an art collector. He wasn't present at their scheduled meeting and Throgmorton wants to know what happened.
He gives you his address. Upon arrival, Reed finds himself in a well kept house, finely and richly decorated. On the ground floor the player can find a Letter to Mr. Throgmorton, and a 40 year old newspaper article
In the basement you can find a statue head that seems to be missing from a statue on the ground floor. Replacing the head unlocks a nearby door with some supplies behind it.
As he walks upstairs, he finds the corpse of Glover - which attracts wylebeast during the investigation.
Inspecting the corpse, the empty space on the wall, the crumpled paper on the table, the bullet holes on the mirror, and the safe lets Reed recreate the scene. Additional evidence can be found by Reed using his Mind's Eye on the magnifying glass on the table in the safe room and examining the painting on the wall opposite the broken mirror in the hallway.
Recreating the scene reveals that there was a robbery. Two armed men broke in and were surprised by Glover while they were stealing. The stolen object turns out to be a mirror.
Two men broke into Herbert Glover's house in Oldgrove to steal a specific mirror. One of them, an experienced thief nicknamed "Squint", proceeded to crack a safe, alerted the owner and got a bullet. The second burglar killed the owner with a knife
Squint mentioned that this is not his first robbery in the district of Oldgrove
Using the information gathered in recreating the scene Reed can go to the Oakmont Police Department to find more information on "Squint" Using the archive (Crimes: Property Crimes, Subjects: Suspects, District: Oldgrove) reed finds Squint's police file which not only reveals Squints identity, Philip O'Connel, but also provides the address of one of his accomplices, Sidney Stokes. Stokes' residence can be found at northern salvation harbor, west of the intersection of Moorland Rd and Salvation rd.
From there Reed goes to the Residence of Sidney Stokes to find more information. Entering there he finds the ground floor largely empty, On the ground floor he finds a Letter from the morgue. Using his minds eye Reed notices a small shrine hidden away under a basin near the end of the table. Taking the bullets from this shrine grants the No Honor Among Thieves Achievement. Heading upstairs reed finds O'Connel, dead on the ground with a knife in his chest. Using his minds eye the knife reveals an unknown woman killed O'Connel and took the mirror. Following the omens reveals a illusory wall behind which is Sidney Stokes. Talking to him reveals that both he and O'Connel were hired by this same strange woman to get the mirror. When they later met with her she killed O'Connel and trapped Stokes behind the illusory wall. Additional evidence can be found using his minds eye on a bottle on a small card table upstairs.
After this Reed reports back to Throgmorton. When reporting to Throgmorton, he is more interested about the thief than the death of Glover. He tells you to continue your search, ending the quest and triggering Through the Looking Glass.