Every quest item tells you whether you still need it. Hover a quest item in your satchel, bank or the market and its tooltip says Needed for: <quest> (in progress), Not needed yet: <quest> not started, or No longer needed (<quest> complete). Trophies and books you keep for good say Keepsake from <quest>. Ordinary items a quest in progress asks for (ore for the smith, herbs for a remedy) get a Quest use line while you need them.
Quest items are marked on their slot. A small brass scroll in the corner means a quest needs it (or will), a star marks a keepsake, and a faded tick (with a dimmed icon) means no quest needs it any more.
Clear finished quest items. A new button in the bank (and in your satchel when you have any) lists exactly which stacks will go, where they are and why, and asks you to confirm. Only items that every quest using them is finished with are removed; keepsakes, books, locked slots and anything with another use are always kept. Quest items have no shop value, so clearing them pays nothing.
Lost a quest item you still need? Ask the person who gave it to you ("I have lost the ..."). They hand you a spare while that step of the quest needs it, as long as there is none in your satchel or bank.
Changed
Quest items no longer pile up. When you finish a quest, its letters, keys and tokens that no other quest needs are handed back automatically, from your satchel and your bank, and a message tells you what went. Keepsakes and trophies (like the Quiet Lamp Badge, Corvane's Seal or the Dawn-touched Feather) stay with you. Quests you finished before this update are not touched: use Clear finished quest items to tidy up.