These seem to be one-time-only quests. However, the object that starts the quest can continue to drop as of this date. Clicking on them after already completing the quest returns the standard "you have already completed this quest" text. You should be able to safely delete the item. Hopefully, Blizzard will update the event to not drop these for you if you have already completed the associated quests.
Quest
Curious Find: Waterlogged Ledger
Quest facts and objectives from the current retail game data.
The highest voted Wowhead comments for this page. They are community notes, not TheWoWDB comments.
I found [item=208734] in the chest which is left after completing WQ Excavation: A Cliffside Full of Caches in The Forbidden Reach.
That is every comment on this page.
Quest facts
The client quest POI data records no map location for this quest, so no map is shown.
Check whether you have already completed this quest
in-game: /run print(C_QuestLog.IsQuestFlaggedCompleted(77763))
Description
<This leather-bound ledger is so waterlogged it's nearly falling apart. Most of it is illegible, but the text that has survived is in an ancient draconic dialect. It appears to be lists and lists of ordinary items, with numbers assigned to them-- perhaps a household accounting book? Eadweard would know how to preserve this find and figure out whom it might belong to.>
Community notes from Wowhead · 2 comments
Top 2 shown aboveThe comments below were written by Wowhead users. They are community notes, not TheWoWDB comments. See them in context on Wowhead.
All 2 comments on this page are shown in Top Comments above.
Mysterious Fragmentx 100
Reward details
Currency: Mysterious Fragment x 100
Obtained by assisting the Azerothian Archivists in the Dragon Isles. Bring them to Provisioner Aristta in Thaldraszus to exchange for items.
Item facts are the current retail client’s (ItemSparse); the specialisations for a pick-one item are the ones the Blizzard quest API lists; faction and currency text is the client’s own. Lowest listed price = the US commodity auction house now.