Homepage to show only posts they have access to view, not all content

Hi,

When a user logs in I don't want them to be able to see posts listed on the homepage that they do not have access to view.

At the moment when a user logs in the home page lists all published posts (I am using the Hatch theme and posts appear as thumbnails/featured images). Obviously when a user tries to view content which is not available on their access level the restricted content page appears. But how do I set Membership up so that they do not see the thumbnails of these restricted posts at all and just thumbnails of the content they have access to view?

Thanks for your help

Damien