Disable a network-enabled plugin for one site

Hello,
We are trying to keep a plugin Network-Enabled, BUT not run on one of our site. That site has its own sub-functions.php.
We tried:

add_filter( 'site_option_active_sitewide_plugins', 'dg_remove_recaptcha' );
function dg_remove_recaptcha( $value ) {
  if ( isset( $value['invisible-recaptcha/invisible-recaptcha.php'] ) ) {
    unset( $value['invisible-recaptcha/invisible-recaptcha.php'] );
  }
  return $value;
}

But while it shows the plugin as deactivated in the plugins’ list, it still runs and inject its HTML code on the site.

Anyone knows how to achieve this?