ReCaptcha Integration error Invalid ReCAPTCHA client id: 0

I use Contact Form 7 with ReCaptcha Integration setup within the plugin. I also use WP reCaptcha Integration to render recaptcha on other parts of the site.

On my contact form, once user has verified the recaptcha and submits the form, a Javascript error appears in the console:
recaptcha__en_gb.js:288 Uncaught Error:
Invalid ReCAPTCHA client id: 0(…)

This exception is thrown when wpcf7 wants to reset the recaptcha:
grecaptcha.reset(value);

However, the mail does get sent after the ajax loader disappear. But as a result of this javascript error, the visitor doesn’t get a response back saying that their message has been sent (e.g. Your message was sent successfully. Thanks.).
Instead the recaptcha remains ticked. And visitors continue submitting their form several times since no confirmation is displayed.

Configuration:
Contact Form 7 4.5.1
Flamingo 1.4
WP reCaptcha Integration 1.1.10