Hi Charline - I agree, assuming you keep the data for the 7ish years required by HMRC for your own accounting, if there's no longer any need to hold it, you must be able to delete it, and, as processor, CB should provide a facility to do this.
Theo, can you check this (with Ruth?) - the company's GDPR announcements cover it's own responsibility over our (user's) own data but I'm not sure there's been any announcement over how it acts as our processor, ie enabling us to comply with our own GDPR obligations as controllers.
Having said that, Charline, you could edit the contact (and any additional contacts) and change the name to ZZ001, ZZ002 etc, remove email addresses etc and archive them, that way their names will not appear anywhere in the system?