<?php

// o HTML que recolheste
$html = '<html>
<head></head>
<body>
<a href="https://w...content-available-to-author-only...e.com/user.asp?ref=fvFCF9D8N4Ak">bubu</a>
<a href="https://w...content-available-to-author-only...e.com/checkout.asp?ref=fvFDGND2MYQ">bubu</a>
<a href="https://w...content-available-to-author-only...e.com/user.asp?ref=fvFCF9D8N4Ak">bubu</a>
</body>
</html>';

// Instanciar o DOMDocument
$dom = new DOMDocument;

// Carregar o HTML recolhido para o DOMDocument
@$dom->loadHTML($html);

// Percorrer o DOM e por cada tag 'a' encontrada
foreach ($dom->getElementsByTagName('a') as $tag) {

    // apanhar o valor do atributo 'href'
    $href = $tag->getAttribute('href');

    // se não estiver vazio
    if (!empty($href) && strpos($href, "checkout.asp?ref=") !== FALSE) {

        // guardar a query string numa variável
        echo $queryString = parse_url($href, PHP_URL_QUERY);  // Resultado: ref=fvFCF9D8N4Ak
    }
}