This padding is calculated dynamically based on aspect-ratio of the embed content. And it is required to make it responsive. The internal content should be filling the space.
Can you give an example of URL that doesn’t?
So I discovered this page that seems to have the issue:
http://www.pmscope.com/marceltj/
The embed code on the page is this:
<div style="max-width: 1566px;">
<div style="left: 0px; width: 100%; height: 0px; position: relative; padding-bottom: 66.4112%;">
<iframe src="//iframe.ly/lTdAPA?summary=true" style="border: none" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true" style="top: 0px; left: 0px; width: 100%; height: 100%; position: absolute;"></iframe>
</div></div>
So something added style="border: none" to an iFrame that made our iFrame style be ignored. So the iFrame goes with default browser sizing and that is what ruins it for you.
You need to find what adds “border:none” and disable it to fix our embeds.
