If you would like to change the visibility of your CV, log into Indeed CV here.
To the right of your CV, you'll see options to make your CV public or private, or to remove your CV.
Public CVs are visible to anyone, however, your phone number and email address are provided only to employers to whom you apply (NB: If you put your phone number and email address in the CV itself, instead of the fields provided, it may be visible to everyone). Your street address and postcode are visible only to you.
Private CVs are not visible (and employers cannot find you). When you set your CV to Private, it does not appear in the search results, but you will still be able to use it to apply for jobs with the easily apply to this job marker.