You guys realize that the way the Web works is by DOWNLOADING files (like .html
files, .jpg files, etc) and viewing them on your computer via the browser,
right?  It doesn't magically read them off your server, the browser would need
direct access to your server's hard drive which would be a security nightmare. 
Instead, the browser requests files from the server, and the server sends them
to the computer that requested them for viewing.

It is impossible to view a web page without first downloading the page and
everything it immediately references to your computer first.  Browsers can
only work by caching the files to a temporary folder, and then processing them
through the web browser.  

To see what I mean, go into your browser's options, and look for a "temporary
files" or "cache files", generally with an option to delete them.  Depending
on your browser you may also have an option to browse them first.  Unless you
regularly clear your cache, you will have a copy of every single website
you've visited in the last few days (though it will be a disorganized mess). 
HTTrack is basically nothing more than an offline web browser - it grabs the
files available to all web browsers and organizes them before allowing you to
see them, rather than downloading the files as you hop to each page like a
normal web browser.

Basically what I'm saying is, if you believe HTTrack is somehow violating your
copyright (whole other discussion, but copyright is violated by distributing,
not downloading), then you also believe that everyone who views your web page
is violating your copyright, and you don't want anybody to see it.  Obviously,
that's stupid, or you would not have a web page in the first place.  

If HTTrack is somehow able to grab files you do NOT want people to see, what
are they doing on your web page? It's public facing and meant for public
consumption, why would you store them there?  If they are meant to be there
but protected (like with membership access), then you need to assess your
security, because if HTTrack can access them, so can anybody else.

BTW, just an FYI, but web browsers like Internet Explorer have had a far less
robust offline web viewing modes for over a decade now.  You're way off base
with this one guys.  HTTrack can't hack anything, it behaves just like a web
browser and nothing more.