In the image of the Ancients (45 SCH quest)

I have deleted the gear I got while doing the quest as I had better gear. Little did I know that I needed to present this gear to complete the quest. I am unable to complete the quest now and I am unable to reset the quest. Is there any fix to this?

If that's the gear I think it is is, you can just go to a Calamity Salvager NPC and repurchase it. There's one in each of the starter cities, the Gridania one is probably easiest though as it's right next to Mih Khetto's Amphitheatre teleport.

I tried that but it did not work, I think it's because you need to complete the quest first.

Oh :(

Sorry if you already tried these things, but is it possible to abandon the quest and restart it and/or go back to the NPCs and talk to them again. Looking at the dialogue of the quest it suggests going back and talking to the NPCs (weavers, goldsmiths and leatherworker guilds) might give you another:

Serendipity: "Wow, you really are as foolish as Red said! He came by earlier and gave me additional mortarboards, saying that you'd probably come back and ask for another. "

Tbh, why would someone discard things he was send out to get?
Does noone ever read the quest dialoge or the intermediate targets?

But in most cases you can just go back where you got the things and get it another time, as long as you don't have it in your inventory somewhere.