Dear Sai,
Sure, there is a way to extract a report each week that identifies tasks completed during that week.
1. In Filter panel select Status field, uncheck all statuses except for 'Complete' and 'Verified', and click OK. (Mind that you can create your own statuses that correspond your workflow better. See Start Up guide: http://www.taskmanagementsoft.com/products/taskmanagerpro/tutorials/startup-guide/setting-workflow.php)
2. In Filter panel select Date Range field, select option Relative 'This Week' and click OK
3. In Filter panel click on 'Save as…' button, select New, enter the name of the filter ex.: 'Completed This Week' and click OK.