If you wish to keep track of your complimentary accounts, there are two ways to accomplish this.
The first way is to collect and store that information from your customers using custom fields. You can add custom fields to the users account without them being able to see it. For example, if you give members access for free, you may want to later see all the users who used those coupons. Adding this checkbox to the members account would help to keep track of comp'd members. When you enter information into custom fields it will optionally show up on the member's My Account page and in the member details area which you can access from the Manage Members screen. Read this article to learn more about how custom fields work.
The second way is to use the PHP interface to locate complimentary accounts. MemberMouse includes the is_complimentary attribute for testing this. You can see all the attributes here: MemberMouse WordPress Hooks
A simple PHP script that could be used as an example to generate a list of complimentary accounts, can be downloaded here.
NOTE–Running a script like this could be resource-intensive, depending on the size of your site. This one just outputs a list of email addresses when run from a browser address bar.