Is there a way to restrict assigned tasks from appearing on a user's timesheet?

Robert - If an assigned task or issue meets the criteria selected under Setup > Timesheets & Hour > Preferences > Pre-Populate Timesheets with, then it will appear on a user's timesheet and cannot be removed unless the user is un-assigned.

Also, remember that if a task or issue has been pinned to the timesheet, it will stay there until un-pinned.

If you have any questions, let me know!

Robert - if you are trying to restrict logging time on the task, my workaround is to change the sharing permission on the task.

I do this for recurring tasks when there are 2 assignees to a task but at some point, only one would pick up the task for the month. By changing their access in advance settings, you can not allow them to log time on the task even if they see the task on their timesheet.