This seems heavily bugged.
(https://i.gyazo.com/7260d5cf0b9a2408ebc395d0be619bee.png)
This is the quest log I received. He will also try to give you a quest that recommends you talk to the Doorkeeper, even if you have already gotten that quest and done so. This doesn't change anything about your log.
Asking him "[Quest] About this House..." makes the dialogue end and nothing happens. For some reason, I was able to go into the house anyways, but the blank quest listed above never updated, changed, and I was never able to turn it in. Additionally, someone came in immediately after me.