How can we remove visibility of email to Line Manager but retain maintaining for Employee?

Summary:

We have introduced the Contact Info card for Line Managers to view contact details of their direct reports (phones and emails)
Ideally we'd like only the Primary/Work email displayed to the Manager in this card. Removing email region completely, and only have the Phone details displayed, then causes an issue in the Employee self service space and removes the ability for the user to update their own email details through the Employee - Personal Information - Contact card.

The add button is available but when using 'Add - Email' - the option disappears, thus not allowing the email address to be added.