Google reCAPTCHA requires keys that are associated with your domain. If the keys don’t match the domain, then you get an ‘invalid’ message where the reCAPTCHA will go.
You need to review how the API works, or use the reCAPTCHA key that you will need to get from Google for your domain.
You can get a free Google reCAPTCHA key here: Start here https://developers.google.com/recaptcha/intro for how it works. Sign up for a key pair here: https://www.google.com/recaptcha/admin .
A plugin that uses/adds reCAPTCHA should have a place to enter your key. Remember that it needs to be associated with your domain.