Not sure if there is a way to change the urls that are pointing to Google for the button images displayed on the Recapture widget but currently they are causing the SSL enabled site to fail a secure connection since they are point to HTTP and not HTTPS. If there is no way to change this now then I am requesting that these URLS point to the HTTPS instead of HTTP.
<div id="recaptcha_btn_container"> <a title="Get a new challenge" id="recaptcha_reload_btn" href="javascript:Recaptcha.reload()"> <img id="recaptcha_reload" alt="Get a new challenge" src="http://www.google.com/recaptcha/api/img/clean/refresh.png" height="18" width="25"></a> <a title="Get an audio challenge" id="recaptcha_switch_audio_btn" class="recaptcha_only_if_image"> <img id="recaptcha_switch_audio" alt="Get an audio challenge" src="http://www.google.com/recaptcha/api/img/clean/audio.png" height="15" width="25"></a> <a title="Get a visual challenge" id="recaptcha_switch_img_btn" class="recaptcha_only_if_audio"> <img id="recaptcha_switch_img" alt="Get a visual challenge" src="http://www.google.com/recaptcha/api/img/clean/text.png" height="15" width="25"></a> <a title="Help" id="recaptcha_whatsthis_btn" href="javascript:Recaptcha.showhelp()"> <img alt="Help" id="recaptcha_whatsthis" src="http://www.google.com/recaptcha/api/img/clean/help.png" height="16" width="25"></a> </div>