ReCaptcha Icon on every page

I use the Contact Form 7 plugin to let users contact me. The form is only on a single page but the ReCaptcha (icon) is placed on every page which seems unnecessary and to frank “ugly”.

There is another thread about this: https://www.ads-software.com/support/topic/google-recaptcha-everywhere/ and it could be possible to remove it with a “hack” but needs a child theme.

Could this (or a better solution) be integrated into Contact Form 7 directly so that we don’t need a custom script? The ReCaptcha should only be inserted on pages with our forms.

The page I need help with: [log in to see the link]