In order to blur your modal template's background, you will need to add following CSS to your website:
backdrop-filter: blur(6px);
To the HTML element with the class="tp-backdrop tp-active".
It will look like this:
The background that is appearing behind each modal is not embedded in the iframe but appended to the DOM. Therefore, the CSS will need to be added to your website directly.
Please note, that the above does not apply to Safari, as this browser does not support it.