One of the elements of GDPR is the Right To Be Forgotten. If we have a ticket that contains a customers PII such as email address/phone number/home address but they no longer want us to store that information we should be able to redact this information on a closed ticket.
My understanding is that this is not currently possible.

Thanks for posting this, Iain. This request has come up in the past, and I've linked your post to that thread in our tracking system, as the previous thread is no longer live.
Other users are welcome to up vote Iain's request and add any supporting details for the PM in the comments below.