How to show reCaptcha v3 just in register page?

I'm building an app with Angular 12 and Ionic. I have protected the register form with the ng-recaptcha package (https://github.com/DethAriel/ng-recaptcha) which uses the Google reCaptcha v3 (https://developers.google.com/recaptcha/docs/v3).

My problem is that the badge is shown in every page visited after the register form.

For example, If I register the page redirects me to the Login page, and the badge is shown there too. I have tried to implement the ngOnDestroy method like this:

  ngOnDestroy() : void{
    if (this.recaptchaSubscription) {
      this.recaptchaSubscription.unsubscribe();
    }
    const element = document.getElementsByClassName('grecaptcha-badge')[0];
    if(element){
      this.renderer2.removeChild(this.document.body, element.parentElement);
    }
  }

This works fine, I get redirected to the login page without showing the badge, but if I try to register a new user I loose the captcha protection. It is like the captcha component is not generated anymore.

UPDATE

To use the captcha I just add the service to the constructor like this

  constructor(...
              private recaptchaV3Service: ReCaptchaV3Service,
...) { }

Then I use it when I need it like this

  onSubmit(): void{
    this.recaptchaSubscription = this.recaptchaV3Service.execute('registerCustomer').subscribe((recaptchaToken) => {
      //Do things 
  });

Also in my app.module I had to add this in the providers section:

  providers: [
    ReCaptchaV3Service,
    { provide: RECAPTCHA_V3_SITE_KEY, useValue: environment.captchaKey }
  ],

What we have done in these cases is not to remove the badge from the DOM, just toggling the visibility, so AfterViewInit - display the badge:

ngAfterViewInit() {
  const element = document.getElementsByClassName('grecaptcha-badge')[0] as HTMLElement;
  if (element) {
    element.style.visibility = 'visible';
  }
}

and of course in OnDestroy we hide it:

ngOnDestroy() {
  if (this.recaptchaSubscription) {
    this.recaptchaSubscription.unsubscribe();
  }
  const element = document.getElementsByClassName('grecaptcha-badge')[0] as HTMLElement;
  if (element) {
    element.style.visibility = 'hidden';
  }
}