Add a custom attribute or note to an abandoned checkout from Offsite Payment App

[DomSnap]

How can we update a note or a custom attribute on an abandoned checkout after we call the paymentSessionReject mutation in our offsite payment app? Or is this not possible?

I have spent some time researching the docs to see if this is possible but unable to find an example of how to do this (if it is possible) using the admin API or the graphql mutations. It looks possible to do this on a cart, however this requires the Cart ID using the storefront API (which we dont have in our offsite payment app flow).

Thanks!