The icons you are talking about are probably home screen shortcuts to Safari.
If the site they go to still has that shortcut icon as a resource, it should come back when you tap the icon and visit the site. If the site no longer has the resource, the icon won't come back.
What you can do is go to the site, and save it to your home screen again; then delete the old one. If the icon has changed, you'll get a new one. If the website no longer keeps a icon resource you'll get a 'probably ugly' little snippet of the site's page.