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.
To update privacy on an existing task, hover over the task and click the edit pencil to the left of the task name. Alternatively, click on the task name and then choose Edit Task to the right of the page.
You will then have an option to again click on the lock icon and select the users you wish to have access from the drop down menu.
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