How do I attach an image without showing it on the webpage?

Aside from using featured images, <img/> HTML tags in the content, etc., WPSSO can also include attached images in the Open Graph and Twitter Card meta tags. Attached images have a link to the Post or Page, but are not displayed by default (unless they are also included in the content). To attach an image to a Post or Page, go to the Media -> Library and upload a new image, or use one that is already listed with ‘(Unattached)’ under the ‘Uploaded to’ column, and click on its ‘Attach’ link.

See also Working with Image Attachments for additional / related information on image attachments.