Hah, this is a bit of a foolish oversight on my part. It is part of the boilerplate text/code provided by Anvil when creating a custom HTML page:
<center style="font-style:italic; color:#888; margin: 3em;">
(Insert your custom HTML here)
</center>
There is a margin of 3em set by default. I just set this to 0 and the “frame” disappeared. The Anvil logo remains on top, but I am sure that is just part of the free tier and it is not really bothersome.