My bad, you’re right. When you already did the quest in a previous difficulty the note won’t disappear and you have to toss it or sell it, but when you read it the first time it should disappear like a regular lore note, if it doesn’t it’s most likely a bug or an outdated game version.
I just did the quest with a fresh character, and I noticed there was a small change to this quest. The item from the chest is no longer a 2x2 quest item, just a regular 1x1 lore note. You still initiate the quest by opening the chest.
Did a quick forum search for Nane’s Stash and found this thread which describes the same issue: Nane's Stash Quest Item Question
As you can see from the screenshots in this thread, the OP has a 2x2 quest item, while the other player has a 1x1 lore note, like myself.
@samir what game version are you using? My guess is you have an outdated version so if you are on Steam you should verify your game files, I believe GOG has a similar function somewhere.