Here are a list of items that I've noticed (and what drops it) that are either marked as a quest item that drop despite not having the appropriate quest, OR Items that are not marked as a quest item in the flavor text (but has no uses other than a quest and is untradeable) OR not being the appropriate timeframe for it to be dropping Jr. Lioner: Silk Feather All Pixies: Cupid's Lost Arrow Chrysanthemum: Korean Folk Town destructible Plants Deep Clock Tower Monsters: (I'm not sure if ALL of them, but I've seen it drop from Death Teddies, Master Death Teddies, Lazy Buffy, and Buffys at the very least): New Year's Present
Addendum: New Years Present drops from Bernard Greys as well. I surmise that other Omega Sector monsters might also drop it
Addendum: White/Purple Ribbon Gift Box drops from Pink Teddy regardless of if you have the associated quest
Can confirm these are still being dropped without the quest active, they're untradeable but not quest items. I also think the Springy Worm ETC you acquire during the Clock Tower Monster Wipe-Out should be quest items instead of just untradeable.