That won’t be possible without making changes to the Recent Posts Widget Extended plugin.
I would recommend that you contact the plugin authors and ask them to consider supporting Photon for the widget images displayed here.
You can open a new issue on their GitHub repository here.
To support Photon, they could use the jetpack_photon_url
filter in their plugin. You can send them this example so they can find out more:
/**
* Add Photon support to any image.
* The jetpack_photon_url filter will allow Photon to serve the images if Jetpack's Photon module is on.
*
* The filter allows you to pass an image URL, and some optional parameters.
*
* @param string $image_url Any image URL can be used.
* @param array|string $args Optional options to manipulate images.
* @see https://developer.wordpress.com/docs/photon/api/
* @param string $scheme Optional scheme in which to return image.
* Accepts <code>http</code>, <code>https</code>, and <code>network_path</code> (no protocol).
*/
$image_url = 'https://mysite.com/img/logo.png';
$args = array(
'filter' => 'grayscale',
'resize' => '600,200',
);
echo apply_filters(
'jetpack_photon_url',
esc_url( $image_url ),
$args,
'https'
);