Body
Overview
Tasks and Activities can be added to the tickets without Start and Due dates.
Issue
When you click on the value it automatically brings up the date/time selector. You can close the selector and type/clear values in the text box by hitting escape button when the date/time selector comes up. Please refer to Below screen shots:

- Click on +Add and choose Task or Task Template

- Fill out the details

- To remove Start date and Due date, When you click on the value it automatically brings up the date/time selector. You can close that Selector and clear values in the box after hitting escape button [Esc].
Once deleted you can fill out the rest of details and save the task .
- Task will be saved without Start and Due date

Troubleshooting
Please check out TDX Service Page if you still face an issue with this process.