I collected the bandage for Chloe Thorn, so my quest updated saying to deliver it, so I wondered what would happen if I deleted it from my inventory.
I was able to go back to Chloe and complete the second objective without the bandage, but it glitched my objectives to what you see below until I relogged

Once I relogged, the quest had reset as if I had never done it.

In addition, when I went back to the locker with the bandage it was no longer accessible (presumably as I have to wait an hour for the map to reset). It maybe a good idea to make certain quest items respawn instantly if lost (through deletion, use or death).

Reported! Thanks!