Old question but must be answered completely. It's very disappointing that it has not been answered in almost a year!
Those images come from either your:
- Twitter card image or
- Facebook opengraph image
I am not 100% from which one, but I am 100% it is from one of the two, or at least the first image that Google finds while reading your page. So keep this in mind.
To add a facebook opengraph you add these meta tags:
<meta property="fb:app_id" content=""/>
<meta property="og:type" content="website"/>
<meta property="og:title" content="My website title"/>
<meta property="og:url" content="https://www.mywebsite.com/"/>
<meta property="og:image" content="https://www.mywebsite.com/images/special/image_og.jpg" />
<meta property="og:image:width" content="640" />
<meta property="og:image:height" content="480" />
<meta property="og:description" content="My website description"/>
Then go to check how it looks on facebook: https://developers.facebook.com/tools/debug
To add a twitter card you add these meta tags:
<meta name="twitter:card" content="summary"/>
<meta name="twitter:site" content="@mywebsite" />
<meta name="twitter:title" content="My website title"/>
<meta name="twitter:image" content="https://www.mywebsite.com/images/special/image_twitter.jpg"/>
<meta name="twitter:image:width" content="200"/>
<meta name="twitter:image:height" content="200"/>
<meta name="twitter:description" content="My website description"/>
Then go to check how it looks on twitter: https://cards-dev.twitter.com/validator
Now ask Google to reindex your page using the URL Inspection Tool here:
https://search.google.com/search-console
https://support.google.com/webmasters/answer/9012289
And to be complete, before you ask for a re-index by Google, add also the special favicon which will appear only on Google mobile search results!!! This is not your regular favicon. This is special. So I suggest adding another line to your page like this:
<!-- GOOGLE MOBILE SEARCH favicon 48x48 MINIMUM!!! -->
<link rel="shortcut icon" href="https://www.mywebsite.com/images/special/favicon.png">
Best to use 'https://www.mywebsite.com/images' a complete URL for all these images. These are all special images for special purposes and have special requirements. Therefore I have them in a special folder!