Let's say you want to hide the scaling buttons on an embed. You can totally do that, because you have full CSS control over your embedded Pens if you're a PRO member.

1) Make a new theme in the Embed Theme Builder

Go there.

Make a theme:

2) Create the CSS you want to apply to the theme.

Think of it as overriding anything you want to override. I want to hide the scaling buttons, so I've found the class name here I want to use.

So the CSS I want to write is:

.scaling-choices {
  display: none;

3) Get a URL to the custom CSS

I could put that custom CSS anywhere. I could upload it to a web server somewhere. I could use CodePen's hosted assets (that way I could edit it as an asset). Perhaps the easiest way is to do it as a Pen, save it, then grab the Direct Code Link. Like hosted assets, I can edit the Pen anytime easily doing it this way.

4) Add that URL to the Embed Theme

Then, when editing your theme in the Embed Theme Builder, drop that URL into the Custom CSS area:

That's it! Now the theme will apply that Custom CSS, and in my case, hide those scaling buttons.