To cancel a reservation, open the wishlist where you reserved the gift and tap Cancel Reservation on that wish — this releases the item so someone else can reserve it.
The person who reserved an item is normally the one who cancels it.
Steps
Open the wishlist link where you reserved the wish.
Find the item you reserved (it shows as reserved by you).
Tap Cancel Reservation and confirm.
The item is freed and becomes available for anyone to reserve again.
Keep in mind
As soon as you cancel, the wish opens up and another gift-giver can reserve it. See "Can two people reserve the same gift?"
The wishlist owner can also remove a reservation. From their manage view, the owner (or a collaborator with at least Contributor access) can remove a reservation on a wish. They'll see the note "We will notify the person who reserved this wish."
Reservations clear automatically if the wish goes away. If a wish or the whole wishlist is deleted, any reservation on it is cancelled automatically. The person who reserved it isn't notified in that case — the reservation is just cancelled.
Cancelling on Wishpicks doesn't undo a purchase. If you already bought the gift at the store, cancelling the reservation here won't return it. Handle any store return with the merchant directly.