If you are signed into Marriott's website, I believe that Marriott uses Secure HTTP or "https" for all of their queries. This would be to "protect" your queries. The issue is that Marriott is redirecting your query over a different port number and your web browser is letting you know this.

If you don't want to see those pesky pop-ups, you could do your searches without being logged in. I suspect there is a web-browser security setting that will turn off the notifications, but I'm not sure that is a good setting to change.