That is so strange. Why would someone pay a company when they can do it themselves for free? When I made a tisha b’av camp I just hung up the signs myself and it didn’t cost me a red cent.
If the payment is more like a courier service, so that someone else can do the legwork of putting it up for you, then theoretically it’s the same as though they hung it up themselves. They paid for the person to hang it up, not for the advertising space.
However, I have no idea why you’d want to take down someone else’s sign unless you’re the shul gabbai or something and you need the bulletin board for something else. If you have a problem, hashkafic or otherwise, with the content of the flyer then speak to the rav of the shul or the people who got the flyers put up.