Posting a URL (link) to LinkedIn causes LinkedIn to fetch an image from that page to use as a "preview" in your LinkedIn post.
This image is pulled from your website's opengraph code in the website header - the "og:image" property, which is generated by the Genesis framework. This is loaded by default by our themes.
The "og:image" property is only present on pages that have a featured image set - this is usually posts and pages, though sometimes can be configured for indexes.
Your homepage, and pages that don't have a featured image set won't have this.
If there is no og:image meta tag set, LinkedIn may simply pull the most "relevant" image it finds - it's unknown how this is determined.
It is possible to set a default featured image, however this is a customization, and not something we offer.
For more information, see: LinkedIn Featured Images.
