Thanks to jwilander for helping me out so much with this. I'm leaving his answer up in case someone else has this problem with version 1.3+, but he helped me in chat, and here's what we did.
I needed to change the username and email address of the user that is now blocked. Meaning, I have to put in different values so that that user can recreate their account, using the same username and email, and the old account sits there, with dummy information.
For this "guide" I'll pretend like my co-workers name is John Doe
Here's how I did it (once again with very patient help from jwilander)
Log into the gitlab omnibus postgres db
Found here
sudo -u gitlab-psql /opt/gitlab/embedded/bin/psql -h /var/opt/gitlab/postgresql -d gitlabhq_production
Connect to the mattermost table
\connect mattermost_production;
Change the username and email values of the broken account
UPDATE users SET email = 'anyTrashValue@example.com' WHERE email = 'john.doe@example.com';
UPDATE users SET username = 'fakeName' WHERE username = 'john.doe';
If you aren't sure what their username/password are, and they aren't available, you can check it using SELECT * FROM users;
or, if you know their nameSELECT * FROM users WHERE username = 'john.doe';
now you can see what email they used.
Log in again
Now resend them a login link to your team, and you should be all done.
Thanks again for the help