Recaptcha blocked on HTTPS page in IE

Our recaptcha elements on our form pages have started to be blocked on pages in IE. Our forms are HTTPS, and IE blocks the recaptchas because they aren't secure content. We have seen a significant drop in volume from these forms in the past few months, and now I'm guessing this is the reason.

Here are the pages in question:
https://vostn.com/referral/
https://vostn.com/new-patient-form/
https://vostn.com/medication-refill-form/

How can this be fixed? Do we even really need recaptchas? I put them on there because it seemed like a good way to block spammers, but how necessary are they for security?

Thanks for your help!

Thanks, David. I've removed the captchas for now, enabled Honeypot, and installed the captcha plugin, but I'm not sure where to go from there... I apologize for my lack of expertise! Is there a custom field I should be working with?

I don't think I'm doing right... do you mean to add the captcha field from the list of advanced fields? I didn't see settings to select the type when I did that, and it was still rendering as unsecure content. What field should I be adding?