How can I removed Powered by WordPress link in wp.login.php without editing core WP files?

In your theme’s functions.php file, add this:

function my_login_css() {
    echo '<link rel="stylesheet" href="' . get_stylesheet_directory_uri() .'/path_to_dir_in_your_theme/login.css">';
}

add_action('login_head', 'my_login_css');

Then just create your custom login.css file that makes whatever changes you want.

To change the link and alt text on the login logo from WordPress.org to the title/url for your site, use these filters in your functions.php file:

// changing the logo link from wordpress.org to your site 
function my_login_url() { echo bloginfo('url'); }

// changing the alt text on the logo to show your site name 
function my_login_title() { echo get_option('blogname'); }

// calling it only on the login page
add_filter('login_headerurl', 'my_login_url');
add_filter('login_headertitle', 'my_login_title');