Mmnyeah, but if you're talking about something you got for free in the first place? I may be reading the OP upside-down and sideways, but I make it out to say:
Some articles came from a free and automated service. These articles contain links. The entity at the other end of the links wants them removed, and doesn't care if it's done by removing the links or removing the entire article that contains the links.
(I originally read it the other way around-- as links from somewhere else to you-- but couldn't get it to work.)
I would worry about the supplier of free links flagging your client's site as uncooperative and quietly removing it from a few lists.