If you reserved a gift by mistake, open the wishlist where you reserved it and tap Cancel Reservation on that wish. The item frees up right away, and someone else can reserve it.
No need to worry. A reservation is just an "I've got this one" marker, so undoing it costs nothing.
Steps
Open the wishlist link where you reserved the wish.
Find the item you reserved by accident (it shows as reserved by you).
Tap Cancel Reservation and confirm.
The item is freed immediately and becomes available for anyone to reserve again.
Common questions
Cancelling is instant. Once you cancel, the wish opens back up — and if you change your mind again, you can reserve it once more, as long as no one else has grabbed it in the meantime. See "How to cancel a reservation"
You didn't buy anything. Reserving isn't buying. Wishpicks is not a shop and never takes payment for a gift, so cancelling an accidental reservation undoes nothing at the store. See "Does reserving a gift mean I've bought it?"
Reserved on a different device? You cancel a reservation from the same place you made it. If you reserved as a guest and then opened the wishlist somewhere else (a different browser or device), you may not see it as yours there. Go back to where you reserved it to cancel.
The owner won't know. By default they don't even see reservations, so an accidental one you've cancelled isn't something they'll notice. See "Can I see if someone reserved my gift?"
And if you can't reach your reservation at all, the wishlist owner — or a collaborator with at least Contributor access — can remove it from their manage view.