This is a PRO feature – you will not see it unless you're using the PRO or tournament version.
Under Officials/Referees (on the Schedule Maker page), click Advanced Options
On the resulting modal, enter the score keeper's name and email, and select score keeper from the dropdown:
You can only add users that have an existing account on the site.
Either a) send them the link to set up an account: https://leaguelobster.com/accounts/register
or b) create accounts via the users dashboard (see help article)
Score keepers will not be listed in the Officials list seen in the first screen shot, but only in the advanced options dialog.
To remove a score keeper / revoke score keeper permissions, simply clear both the name and email fields and click save.