How do I change the post title’s link on the posts page?

Use the post_link filter hook:

add_filter( 'post_link', 'wpse_change_post_link', 99, 3 );

function wpse_change_post_link( $url, $post, $leavename = false ) {
    // Can't fill these conditions since you didn't specify them...
    if ( 'my_post_type' === $post->post_type ) {
        $url=""; // Your new URL...
    }

    return $url;
}