No. Not with a button, not with a setting. Reservations are kept where your account can't read them.
Do my friends need an account or an app?
An account, yes. An app, no. They open the link, sign up in a minute, and reserve. The account is what keeps each reservation theirs, and hidden from you.
What if a friend changes their mind?
They un-reserve in one tap and the gift is free again. You're not told.
Can I change my list later?
Until a week before the day — sooner if you made the list at short notice. Then it locks, so nobody buys something you've just removed.