I decided to hide the badge on all pages except my contact page (using Wordpress):
/* Hides the reCAPTCHA on every page */
.grecaptcha-badge {
visibility: hidden !important;
}
/* Shows the reCAPTCHA on the Contact page */
/* Obviously change the page number to your own */
.page-id-17 .grecaptcha-badge {
visibility: visible !important;
}
I'm not a web developer so please correct me if there's something wrong.
EDIT: Updated to use visibility instead of display.