There are standard commands in HTML (a programming/presentation language that makes all web pages work) that let you include external web pages within your own web page. However, if you do this without permission it's a violation of copyright laws.
There is a remote possibility of a security concern. The other site could theoretically be configured for what's called a Man In The Middle attack wherein they present HST's login page and when you login they could acquire your username and password, or possibly copy your HST cookies. I think it unlikely they are doing this though.
More likely is they are after free money by monetizing HST on their site.
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