That’s odd the theme is adding class="table table-striped" display="table"
to the initially rendered calendar, but not adding it to the calendar that is rendered by the ajax request.
My guess is, that in a bid to use bootstrap styling with WordPress mark-up, with minimal changes to any CSS stylesheets, they’ve injected bootstrap classes into the rendering of the widget. The ajax request just renders a calendar rather than widget, which might explain why the theme doesn’t inject its classes then (it’s not a widget context).
I’ll look into this.