Unable to delete option

You’re almost there… If you send the request to admin-post.php, then only your callback will print the response. And since your callback doesn’t print anything, then you’re getting blank screen.

Most of the time what you want to do is to perform a redirect inside such callback:

public function kh_update_media_seo() {
    delete_option('myoption');
    wp_redirect( admin_url('admin.php?page=mycustomoptionspage') );
    exit;
}
add_action( 'admin_post_my_media_update', 'kh_update_media_seo' );