You could use a form plugin instead of the default contact form. Just add the form shortcode to the contact form field on the listing. Many form plugins, like Ninja Forms or Gravity Forms, include an anti-spam feature for custom forms.
You should upgrade the plugin with a captcha. it would be awesome !
By the way, great plugin.
If you have a lot of listings, entering a custom form shortcode for each one is not ideal — there should be a global setting for this, following an option to disable the built-in inquiry form.
The real problem behind the spam issue is that listings have vulnerable contact forms by default, and there is no way to disable, replace, or modify them to be more spam-resistant without creating a new listing page template. At minimum the contact forms should have an option to disable them in the plugin settings.
An option to using WP comments instead of a mail form might be a good path to take since there are many existing spam defenses for comments.
Related issue in the WP Listings GitHub repo: https://github.com/agentevolution/wp-listings/issues/10