If you’ll never get around to that task, then having it on a todo list won’t help. It will hurt. That open loop will take up valuable cycles in your mind that you could spend on the tasks you would rather do. Migrate that task to a “To-Don’t” list instead.
Your brain won’t let you simply “forget” about a task you won’t complete, especially if you felt or still feel obligated to perform it. Your brain will keep bringing it up, be it as an express reminder, a vague feeling of uncertainty, or as an imperceptible but impactful increment to your overall level of stress. You have to tell your brain that it’s okay to let that task go. Of course, you have to want to free yourself of such a task. As long as you feel that you “should,” “ought to,” or were “supposed to” do it, then the task will haunt you.
You don’t have to rationalize your choice to reject a task and, indeed, there’s little point to doing that with yourself. Even if your parter or manager or parent needs an explanation, you can’t fool your subconscious so easily. Like how smiling makes you feel happier, making a physical effort to declare a nagging task as “resolved” will help. Set aside a “To-Don’t” checklist, ideally a paper one, and write down what you have decided against doing. Next time your mind brings it up, you can go to that notebook and remind it that the task is a done deal. When others ask you about the task, you can tell them with sincere conviction that it won’t be done. They may well appreciate the closure such a declaration brings them, too. Your future self will certainly appreciate it.