Problem

The Jira Core mail handler doesn't handle adding comments to Service Management requests the same way as the Jira Service Management mail channel does, e.g. depending on configuration, comments may be added as internal instead of visible in the Customer Portal. However, some Service Management admins do not want to have email be an available channel for creating new Requests. 

Cause

 It's not currently possible to configure Service Management email channel that will only handle comments/updates but not new requests.  See also, for example:  JSDSERVER-3697 - Getting issue details... STATUS

Workaround

Configure an Automation rule to automatically resolve requests that come in via the email channel, after having added a comment referring your users to the Customer Portal.  You can extend this using an add-on to go so far as to delete the requests that come in via email if having them lingering resolved is undesirable. 

1. Setup a new Request Type and if using JSD 3.2.0+ make it hidden from the Customer Portal. 
2. Ensure that a transition exists from the first Status in the workflow to the Resolved/Closed state. 
3. Define an automation rule that will
   1. Add a comment directing your customers to the Customer Portal.
   2. Transition the issue arriving via the mail channel immediately thereafter. This could be done using a WHEN condition that matches the specific Request Type or the request-channel-type
4. Setup Mail requests normally, using the specially created Request Type.

If required, you can implement or extend this using an add-on that introduces more robust automation features that will allow you to have the requests be deleted as they arrive instead of simply resolved.