Do these forms HAVE to have the CAPTCHA?

Or is there a way to disable that?

The captcha shows when submitting the form since you're using the source code, maybe you made some changes to your form in the builder and did not update the code so I would suggest you to re-embed your form with a fresh copy of the source code.

You can also embed it using a different embed method such as the iFrame code, do note that you could also customize your form with CSS code so it looks the same as your webpage. 

Hope this helps.