The Swirling Vial

You can not turn in [item=129747] after the end of the Timewalking Event. You will have to wait until it comes around again.

See this post related to the vendor [npc=98685]

Check your quest completion during the event. Useful for alts to quickly check status.

The Swirling Vial

/script print(IsQuestFlaggedCompleted(40168))

• 
  
• TRUE if completed.
• 
  
• FALSE if you have not yet completed it during the current event.
• 
  

Edit: As noted by Nerravar, turn in the quest to [npc=98685] in Shattrath City, Outlands.

Side note: This is a basic script to check quest completion. Run it from your chat window as you would any other command in the game. Similar, albeit more advanced scripts, also exist to check for NPCs killed each week such as the World Bosses in Draenor.

You can also substitute the 5-digit quest code above with other quest codes found on Battle.net and here on Wowhead to check their completion status.

Blizzard should consider leaving the quest turn in npc active at all times. I got this on the last day of the timewalking event and had no time to turn it in. Now, I'm stuck with this item in my inventory for three months because that's how long it takes Blizzard to cycle through all the timewalking events, pvp events and Legion dungeon events. This is pointless, considering that most quest givers are active 24/7.