From the Jira home screen click Projects (1) in the main navigation menu and select the project (2) for which you would like to revoke the Intercom connection. After the project page loaded select Project settings (3) in the left-hand menu then scroll down to find and click on Intercom integration. This loads the Intercom integration settings page.
Click the Revoke Connection (1) next to the green label that says Connected.
Revoking the connection to Intercom will not delete your Intercom conversation links or remove your project configuration, i.e visible fields or notification settings. If you ever decide to reconnect your Jira project the configuration will be back in place just as it was. Note, that existing conversation links will only be working, however, if you are connecting back to the same Intercom workspace.