Yes, completed tasks can be reset to "not completed" status.
There is a toggle switch at the top of the Checklist page that controls whether or not completed tasks are visible. Be sure it is turned on so you can see completed tasks in your list.
To mark a completed task as incomplete, you can click the checkbox at the left of the task in the list. Alternately, you can click to open the card, and uncheck the box at the top to mark the task as incomplete.
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