Most of us have similar cases and we usually keep the solution as "don't include the items in the backlog/sprint" - you don't want them in there because the backlog is for the development team, and these items need doing outside the team.
Often, people will simply do it with a separate project, changing the project plan so that it includes the dev project and the external project, and using links between issues in the two projects to show relationships.
But another way to do it (especially if you're putting all the issues into one project) is to differentiate the external issues somehow, and then set up the board to ignore them.
An obvious way to do this would be to have your project have a set of issue types such as: Issue, Bug, Improvement, external-task, and then have a board set up for the developers that says "Project = XYZ and issuetype != external-task. You could do this with components, labels or pretty much any other field you wanted too. And even set up a separate board for the external users.
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