When a cPanel user is logged in and accesses the Email Accounts section, there is a "Check Email" button on all email accounts that allows access to the listed Webmail accounts. Can this be removed?
There is not a feature in cPanel or WHM to disable this functionality.
It is beyond the intended design and use of cPanel to provide any level of privacy between an admin-level account, and a non-admin level account such as between the cPanel user and an email user. It is intended that the cPanel user is an admin within the context of the cPanel login session, and the home directory. As an admin, the cPanel user has full access to everything stored within the home directory, including emails. Implementing this control would present a false sense of security and privacy to email users, as the cPanel user has direct access to all emails and email accounts stored in the home directory.
However, a custom theme or style can be created and implemented on your server that can hide this option. More information about theming your cPanel can be found here: How can I customize the cPanel theme or add my own branding?