Open the wishlist where you reserved the gift and tap Cancel Reservation on that wish. The item is released, and someone else can reserve it.

Normally the person who reserved an item is the one who cancels it. The wishlist owner can also remove a reservation from their manage view, as can a collaborator with at least Contributor access. They see a note first: "We will notify the person who reserved this wish."

Reservations clear on their own if the wish or the whole wishlist gets deleted. The person who reserved it isn't notified in that case; the reservation just goes away.

Cancelling here doesn't undo a purchase. If you already bought the gift at the store, cancelling on Wishpicks won't return it. Sort out any return with the merchant directly.