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.
Nothing to worry about here. 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 mistake (it shows as reserved by you).
Tap Cancel Reservation and confirm.
The wish is free again straight away.
Change your mind a second time? You can reserve it again, as long as nobody else grabbed it in between.
Good to know
You didn't buy anything. Reserving isn't buying, and Wishpicks never takes payment for a gift, so cancelling an accidental reservation undoes nothing at the store.
Reserved on a different device? You cancel from the same place you reserved. If you reserved as a guest and then opened the wishlist in another browser or on another device, it may not show as yours there. Go back to where you reserved it.
The owner probably won't notice either way, since by default they don't see reservations at all. And if you can't reach your reservation, the wishlist owner or a collaborator with at least Contributor access can remove it from their manage view.
Related
"How to cancel a reservation"
"Does reserving a gift mean I've bought it?"
"Can I see if someone reserved my gift?"