World of Warcraft Item Restoration - Quest Items

Can you restore heroic dungeon daily quest items through item restoration service?

I accidentally abandoned the “Proof of Demise: Ingvar the Plundered” quest right before returning to Archmage Lan’dalock instead of closing the quest log and the Axe of the Plundered disappeared from my inventory.

I tried to restore the item through the restoration service, but it’s not listed there.
I tried to log out several time, clear the character selection and select the character again, yet the “Quest” category does not show any items.

Is it possible to restore quest items lost this way or my absent-mindedness just cost me 2 Emblems of Valor and 48 gold from wasted daily as I clearly cannot run the dungeon for the quest item again till the instance lock is lifted and new daily quests provided.

The item restoration will not restore destroyed quest items and Blizzard cannot assist you with either the quest item or quest progress.

It appears you’ll have to wait for the next instance lock.

OK, it’s my own fault that led to the loss of the item.
I just wonder why there is quest item category in the item restoration service if you can’t restore quest items.