This is currently wrapping the actual form in the source code:
... scripts and styles ...
... title plus form code...
... some script ...
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! :)