Browsers do not remember that your site is only on https. The first step of a visit can still go over http.
Without the HSTS header, someone on the same open wifi can step in during that first step and send the visitor to a fake page. With HSTS the browser goes straight to https every time.
This is part of the security check, a separate check next to the crawl, in Studio and Bureau, and only on a site you have verified. Snaglist only looks at what any visitor can see from outside. It never logs in, guesses no passwords and sends no attacks. It reads the response headers of the homepage and checks whether Strict-Transport-Security is there.
In the report for your client this appears under the heading "Browsers do not remember that your site is secure". When everything is in order, the report says: "Browsers remember that the site is secure (HSTS)".
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