What lothsun said will modify the image size on the site, but it will still end up using the original image (image.jpg, for example) instead of a resized image (image-140x140.jpg).
What I think piskvorky is asking about is a way to modify which thumnail size is chosen, similar to the second variable in get_the_post_thumbnail
<?php echo get_the_post_thumbnail( $post_id, $size, $attr ); ?>
In theory this following modifications should work.
In simple-staff-list/_inc/user-view-show-staff-list.php modify line 90 from
$photo_url = wp_get_attachment_url( get_post_thumbnail_id() );
$photo_url = reset(wp_get_attachment_image_src( get_post_thumbnail_id(), 'staff-thumbnail' ));
In your child theme's functions.php file add the following (modify the dimensions to fit your needs)
add_image_size( 'staff-thumbnail', 140, 140, true );
Additionally, if wordpress can't find the proper image size, it should fall back to the original automatically.
Personally, this is a change I'd love to see added the the plugin permanently, as the modification to user-view-show-staff-list.php will be lost of the addon is updated.