Within Teamwork, you can set the privacy on a task so that only certain people on the project are able to see it.
To set privacy on a task when the task is being created, click the privacy tab (lock icon) and choose which members of the team you wish to have access to it.
You can use the search field at the top to locate specific people. Click the filters button on the right for additional options on who should be selectable in the People and Teams tabs.
To update privacy on an existing task, hover over the task and click the edit pencil to the right of the assignee.
Alternatively, click the task name and then choose Edit Task to the right of the task details view.
When the task is in edit mode, click the privacy tab (lock icon) to update who can see the task.
Note: Site administrators in the owner company will always be selected (gray), as their permissions override privacy by default and they will always be able to see the item.
For more information, see: Setting Privacy on Task Lists