Remove “Edit Link” next to “Publish immediatley” when adding a new post

Here is one idea to hide the Edit link via CSS:

function wpse85434_hide_editlinks() {
    if(!current_user_can('manage_options')){
        // only for non-admins
        echo "<style>.misc-pub-section .edit-timestamp{display:none !important;} </style>";
    }
}
add_action('admin_head-post.php','wpse85434_hide_editlinks');
add_action('admin_head-post-new.php','wpse85434_hide_editlinks');

I use !current_user_can('manage_options') so it will be visible for the admin.

Before:

After: