Hi Patrick,
When you enable 'Google captcha' option in the contact form of T4 Builder, it will take the captcha option that you set in Global Configuration of your site.
As I can see that you're using 'CAPTCHA - reCAPTCHA' now, if it throws error: invalid domain, you need to check the keys of captcha in CAPTCHA - reCAPTCHA plugin again, or consider to generate a new key.
Regards