If you start the quest chain to unlock the Archivists’ Codex rep by going straight to Scholar Roh-Suir in Seeker’s Quorum, without looting/using the Researching Korthian Relics quest item, you will continue to loot the item from treasures and rare mobs in the zone. You cannot use the item as it will tell you “You have completed that quest.” but you will continue to have the item drop for you if you delete it, even after you complete the quest chain. If there was a way to remove the item from the loot table after you unlock the Archivists’ rep, even if you never used it to start the quest chain, that might fix the problem. Either that, or remove Scholar Roh-Suir’s quest marker from the map so you HAVE to use the item to be able to start the quest chain to unlock rep with the Archivists’ Codex.
It’s nothing game breaking, it’s just annoying to keep looting an item you can’t use.