Hide the event registration link to non-members (or those not logged in)

We have a number of events that we only want to display the zoom and registration link to users that are logged in. However even when I use page protection through a memberpress rule the event link if entered will still display publicly. Is there a way to hide the link (usually entered under Event details–>links ) to display only to those that are either a member (or logged in if membership is not possible)

The page I need help with: [log in to see the link]