We currently do not have a feature that prevents Public resumes from being searchable on other search engines.
Resumes set to Public are visible to anyone, however, your phone number and email address are provided only to employers to whom you apply. Your street address and postal code are visible only to you.
Private resumes are not visible (and employers cannot find you). When you set your resume to Private, it does not appear in search results, but you will still be able to use your Indeed resume to apply for jobs with the Apply Now button.
If you would like to change the visibility of your resume, log into your account here and select the Private or Public option (top right, below View Resume).