Michelle,
I am moving this post to our Customization section as it would require a Validation Rule to not allow a user to change the state of a Task (that is not set as executable) to Marked as complete or changed at all if you wish. It would look something like this...
1 - Create a Validation Rule at the work item level (this will take affect for projects, milestones or tasks). This validation rule will not allow the change if the criteria is met. For further clarification, we suggest you register for one of our Office Hours Webinars (see the link-> http://www.clarizen.com/resources/online-demo.html#second ).These are great resources for free consulting with our Customer Success Managers that can provide visual examples and answers to your questions.
2 - Another option is you can remove the ability to set status as complete via Profiles if that is something worth trying. Here is more information on Profiles...
Video Tutorial: https://success.clarizen.com/entries/88326538-Clarizen-Profiles-Tutorial
User Manual: http://usermanual.clarizen.com/profiles-overview