It's semi-intentional but we may be able to change it.
For now the workaround is to set the Template to:
<div class="block-body block-row">
<!-- your HTML here -->
And then check "Advanced mode".
This removes the default HTML which would surround your HTML (including the header) but replaces it with the basic block HTML without a header. You just need to replace the <!-- your HTML here --> bit with your HTML.