Thank you for the explanation @chcw. It helps. I now understand what you are seeing:
1) failed logins: in this case the plugin reports system because no user is associated with the failed login. For example, if someone tries to login with user XYZ and you do not have the user XYZ on your website, than that is considered as a failed login with an invalid user.
2) Modified files: the plugin has its own file integrity monitor to detect file changes on your website. When file changes are detected, and they are not done by a user, but for example when someone uploads a file, the plugin cannot report or associate a user with such change, so in that case, the System is reported.
I hope the above clearly explains how “System” is used in the plugin and why you cannot exclude it. Should you require any further clarification, please do not hesitate to ask.
Have a good day.