Hi Polly,
When you add a customer to your service desk, you are also adding him to the Service Desk Customers role of the project.
You can remove people from this role through the project settings and then selecting Users and Roles. Or from the Customers list of your service desk, click the link to remove customers in the top right of the view:
Note that - as a project admin - you cannot remove a customer's account from the JIRA instance, but removing it from the mentioned role will remove the user's access to your service desk project.
If his/her account needs to be deactivated, you should ask your JIRA Administrator to do it for you.
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