Hi Jennifer,
It's not possible to delete an assignment submission. I personally really like that because there is no way an instructor could accidentally or even intentionally remove something. I see that as protection to the teacher in case a student claims the teacher wasn't fair to them. Re-submission works for students to submit a course assignment if they submit the wrong thing and maintains a paper trail so that there is a record of what happened.
For your example where the To Do list keeps telling the instructor to grade something, it's possible to dismiss that alert from the Dashboard and course home page by click the X to the right of it. This will dismiss the item until another one get submitted.

Rick
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