LearnWebDesignOnline.com is proudly hosted by Hostmonster.com

ZenCart has a built-in contact form available at ...
http://www.example.com/index.php?main_page=contact_us
where example.com is your domain name.
Even if you removed the "contact us" link from your store menus. People who knows ZenCart can still access your contact form simply by typing in the direct URL to the contact form (as shown in above).
The contact form looks like ...

If you don't like the use of contact forms for security reasons or because the sender of the form can easily poses as another person by inputting another person's email address, etc, then it is possible to disable the contact form by commenting out the code in the file
/includes/templates/template_default/templates/tpl_contact_us_default.php
as shown...

Of course, if you disable this built-in contact form, you would have to add a contact information page of your own (perhaps with an EZ-Page) so that customers have a way to contact the store owner.