Is it possible to modify the media library admin screen?

That area of all admin screens is where admin notices are displayed, so you could generate an admin notice.

Here’s a suitable function and hook:

function wpse_233031_admin_notice() {
    ?>
    <div class="notice notice-info">
        <p>Your message here!</p>
    </div>
    <?php
}

function wpse_233031_hook_admin_notice() {
    add_action( 'admin_notices', 'wpse_233031_admin_notice' );
}

add_action( 'load-upload.php', 'wpse_233031_hook_admin_notice' );

/* Edited out anonymous function callback, 
   which not only requires PHP 5.3 but is poor WP practice as
   it prevents removal of the function from the hook
*/

Every admin page fires a unique hook of the form load-{unique-string-for-this-screen}. For top level admin pages it takes the form load-{filename}. On the load-upload.php hook we hook into admin_notices so that your notice only appears on this screen.

You should add a class of notice to your div and one of notice-error, notice-warning, notice-success, or notice-info to get the standard WP styling. (If you add a class of is-dismissible WP will supply you with a closing icon, but I believe you need to do the heavy lifting of dismissal and storing dismissed state yourself.)

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