Remove 'textwidget' class using functions.php file?

Hello,
the textwidget class is there to maintain compatibility with the WordPress native text widget. Actually there’s not a simple way to change that without hacking the plugin’s source. Moreover unfortunately WordPress doesn’t have a filter hook aimed to modify widget output on-the-fly. There are workarounds for that, but they’re not so handy (i.e. the Widget Logic plugin has such a filter hook internally).
I think the best solution is to modify our plugin’s source, by adding one or more filters / hooks, in order to allow for better flexibility. I will update this topic when this feature will be available.