Problem: When attempting to remove contacts from an incident, they cannot be removed, even though the email@example.com account is associated with the groups that have permissions to remove them.
Cause: Rights and permissions to change contacts have not been extended to groups. This is a known issue
Workaround. At this point, the only known workaround is to explicitly grant full incident edit permissions to a specific user. This will allow him to edit contacts for that incident only. This will only allow that user to edit contacts for this incident only.