This is currently wrapping the actual form in the source code:
<div style="display:none;">
... scripts and styles ...
<div id="subscribebox">
<div id="subscribetopbox">
... title plus form code...
</div>
</div>
... some script ...
</div>
Now, to take control over the FancyBox frame size and scroll bars (in this case) you can give the div with the ID "subscribebox" some parameters. I'd try somehting like this:
<div id="subscribebox" style="width:600px;height:400px;overflow-x:hidden;overflow-y:auto;">
Change the width and height to your liking (the actual form width is about 600px I believe, but you can give the frame any other size) and if you need to, you can change the values for overflow-x and overflow-y depending on your preference to "scroll", "auto" or "hidden".
Do not forget to test the actual submission process and how a failed validation or success message might influence the form size (and subsequent scroll bar behaviour) after submit.
Hope that helps and I thank you VERY kindly for you more than generous donation! :)