If you want to clear a Task that's been set against a Contact, you can do this one of two ways:

Certain statuses of other records (Opportunities and Problems) may require a Task before the window can be closed, so the below functionality will only allow you to add notes and change the Task user.

With the Contact open, you can see who the Contact is currently assigned to in the Communication tile on the right-hand side if you're using a large screen, or at the bottom of the page on a smaller screen.

Clicking the 'Next Action Due' button will open the Task window and allow you to clear or amend the Task. 

You can add a note in this window and then click the 'Clear Task' button to remove the Task.

If you don't fill in any notes on the Activity window, pressing 'Clear Task' will add a default 'Task Cleared' note for you into the text box.

Once happy with information, click 'Save', and this will clear the Task and update the activity page. 

By clicking on the 'Add your reply here...' section, it'll open up a text box for you to enter in any notes that you wish to add when clearing the Task.

Once happy with the message, you can click the 'Assign Task' button. This will open the Task window. 

Clicking on the 'Clear Task' button will remove the Task from the currently-assigned user. 

If you didn't fill in any notes on the Activity feed, pressing 'Clear Task' will add a default 'Task Cleared' note for you in the text box.

Please note: If the Clear Task button is greyed out, this is because the record that you're trying to clear the Task on still has an open status that requires a Task to be set first. In this instance, you'd need to close the Opportunity or Problem using the status drop-down to then be able to clear the Task.

Once happy with the information, click 'Save' and this will clear the Task and update the Activity feed.