Open the wish on your wishlist and choose Delete. It's permanent, and there's no undo for a single deleted wish, so have a second look before you confirm.

Deleting it cancels the reservation. The person who reserved it isn't notified; the reservation simply ends along with the wish. That's different from removing only a reservation, where the person who reserved it does get told.

If you want to keep the item on the list but show it's handled, mark it as fulfilled instead of deleting. The owner or a collaborator can do that, and the wish stays put with a flag saying it's taken care of. Handy when you've already received a gift but still want the record.

Deleting needs Contributor access or higher on the wishlist. As a Contributor you can delete the wishes you added. See "What's the difference between Full access and Contributor?" in the Shared Wishlists collection.