<div class="card" data-component="card" data-options='<div class="customisible-test"><h4>Customisible</h4><ul><li>Image</li><li>Header</li><li>Secondary copy</li></ul></div>'>
<script>
const str = document.querySelector(".card").getAttribute("data-options");
alert(str);
</script>
Вариант
<div class="card" data-component="card" data-options='<div class="customisible-test"><h4>Customisible</h4><ul><li>Image</li><li>Header</li><li>Secondary copy</li></ul></div>'>
<script>
const str = document.querySelector(".card").dataset.options;
alert(str);
</script>