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The new homepage, which went up many months ago, is an .shtml file extension... That file itself is not indexed in the Google listing, rather, it's just the generic homepage URL that doesn't reference a file extension...
Why wouldn't Google update the description in the SERP?
It seems there's been a problem with the site. The internal pages show up as backlinks when you do a backlink check for .shtml but not when you check backlinks for the homepage with just the forward slash.
They've been using the link back to the homepage as index.shtml with the relative URL, they've changed it to be the absolute link but Google hasn't picked up the backlinks right yet. It's been about two weeks since the change was made.