Since most browsers won’t show mixed https/http content now, it would be nice to use https for the recaptcha on the registration page if the registration page is served via https. This can be done by changing line 911 of pie-register/classes/registration_form.php from:
$data .= recaptcha_get_html($publickey);
to
$data .= recaptcha_get_html($publickey, NULL, is_ssl());
(well, that always uses ssl, you’d want to test and use ssl as appropriate).
back on May 14th, 2015 Mohin Abbas said “We will definitely add this in our future release”, but looks like it didn’t get added in.