Even though there currently isn't a TrustedSite app for Squarespace, you can easily add the trustmark. You can easily add the floating trustmark to your SquareSpace site.
In your SquareSpace user portal click on Settings → Advanced → Code Injection.
Scroll down to the footer box and paste the main code.
<script type="text/javascript" src="https://cdn.ywxi.net/js/1.js" async></script>
Save your changes. Please allow a few minutes for the floating trustmark to show up on your website.
Learn more about code injection.