I'd be interested if there's research showing whether a one-off popup gives more signups or more annoyance. The marketing people seem to think it's better to have it there.
I agree it's hard to close, I'll see if I can do something about that. It shouldn't keep coming back once closed, which browser are you using? Although it does come back if you refresh the page. I might be able to do something about that as well.
I just noticed that this kind of pop-up appearing is a trigger for me to close the page. I immediately get the feeling that I got the basic idea of that page.
Personally, those popups are an immediate close tab for me. If you have no confidence in my wanting to sign up for your news letter after I've seen your content, I don't want to bother with your content at all.
You should ask your marketing people to back up their beliefs with research. While you are waiting think about how you react on other sites that use pop-ups. For me it’s an insta-close. YMMV.
I agree it's hard to close, I'll see if I can do something about that. It shouldn't keep coming back once closed, which browser are you using? Although it does come back if you refresh the page. I might be able to do something about that as well.