"A Relic Reborn" Question: What happens to the weapon you turn in?

Ok, I'm a freshly made level 50 White Mage, and just finished my Main Storyline earlier today, and more or less by accident stumbled over the Relic Weapon quest.

I met with Gerolt and found the Thyrus weapon in the U'Ghamaro Mines as well.

Now he wants a Madman's Whispering Rod with 2 Quicktongue III materia.

So here's my questions:
What happens if I turn that weapon in? The Madman's Whispering Rod. Will it be gone or will I keep it for now?
If I get it back, and I turned in a HQ version, will it still be a HQ version?

The reason I ask this is simply: I'm currently using a HQ version of said staff. If it's gone afterwards and I don't get it back, then it would be better to just get a new non-HQ staff and use that for the quest.
I know the quest itself is still another hundred steps till I actually hold Thyrus in my hands for real, so I don't wanna throw away my actual weapon just yet.

u lose it..

Yes get the NQ version instead for quest, cheaper and works just as well.