This is a sample script for retrieving screen shots of sites using Google Apps Script. In order to retrieve the screen shot, here, I used PageSpeed API.
When you use this, please copy and paste the following script, and set an URL you want to retrieve a screen shot.
var siteUrl = "### URL you want to retrieve a screen shot. ###";
var url =
"https://www.googleapis.com/pagespeedonline/v4/runPagespeed?screenshot=true&fields=screenshot&url=" +
encodeURIComponent(siteUrl);