If you are using a regular moodle assignment and have it set to use group submission settings where only one member must submit the file, when one the file is submitted, only the user who submitted the file has their status updated saying "Submitted for grading." All other users in the group retain the "No submission" status.

Mind you, this is their individual submission status. The "Group submission status" reflects that their group has submitted the assignment.

I propose that if in an assignment's group submission settings, "Students submit in groups" is set to "Yes" and "require all group members to submit" is set to "no," the assignment grading page should leave out the individual's "status" column since it is not relevant and does not reflect a proper status. In this case, only the "group submission status" column is relevant.

An additional downside to leaving the individuals submission status visible is that if the due date has passed, the grading page of the assignment will show that anyone who didn't submit a paper for their group is overdue (see attached file).

Replicating this is simple:

1. create some groups in a course and add users to them.
2. create an assignment. Set "students submit in groups" to "yes" and make sure that "require all group members submit" is set to "no."
3. Submit a file as one of the students in a group.
4. Check the submissions page of the assignment and you will see that only the single student who submitted the file has their individual submission status set to "submitted"