Remove Comments on Pages, NOT on Posts!

You should be able to do it using CSS – a link to your site is needed to help with this. Also, do not modify theme files – your changes will be lost when the theme is updated.

See if adding this CSS works:

.page #respond, .page #comments {
    display: none;
}

BTW, you may run into compatibility issues if you are not able to update the theme…

But if I update my theme, all my personal adjustments on the theme will be lost (and I really don’t want that 🙂 )

That’s why we widely recommend using a Child Theme to modify a theme:

http://codex.wordpress.org/Child_Themes