Akeeba Backup at least in the past has absolutely altered database data. It used to completely break CB database when restored. I've no idea what else it maybe doing to data, but I would assume it should just do a simple database drop, create, followed by inserts.
For CBSubs a Basket is an Invoice. So if a Basket does not exist for a subscription (e.g. those given from backend) it's not going to display under Invoices. If the user id of the basket no longer matches the user themselves then again those invoices won't show (it's possible restoring a backup broke the user ids, but I can't be certain). Check within _cbsubs_payment_baskets and ensure the user_id column still matches your users.