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Outside of the Asylum
I believe item cards are generally kept, unless the cards say otherwise. The ones with the red banner are used during combat, so they go into your hand (along with punch/escape/dodge), and you get them back after combat. The ones without red banners tell you when they are played & what to do with them. Sometimes another card effect will tell the hunter to discard a particular item too.
Both the LtP + RR are very short on rules regarding "Item Cards", and this is about the only semi-relevant part. Generally you'll be told when to discard them though...
Learn to Play, pg 10 wrote:
Item CardsEvent cards are discarded when played (not sure if there are any exceptions - I guess that would be written on the card though).
When a hunter draws an item card, he takes the top card from
the item deck and places it in his hand. Most hunter cards can
only be used in combat ( see “Combat” on page 12). These
cards each contain a banner. Item cards without a banner
describe when they can be played.
Rules Reference, pg 8 wrote:
+ Event cards that are played or removed from a player’s hand
are discarded faceup.