You DID build the site so a “created by…” or “designed by…” link is not anything that they can sue you for unless it is clearly spelled out in the contract that it would not be allowed.
Secondly, often decisions in court are made based on “trade custom” and on the Net, it is definitely trade custom that many major corporate and business sites do include a “designed by…” link if the site was not done in-house.
You are under no compulsion whatsoever to tell them what software you used but I would offer them a suggestion … Microsoft FrontPage — heee, heee, heee. That ought to fix them real good and make them appreciate you more. ;o)
Lastly, as you know, most all things done on the Net are based on standards which the company can learn about and modify if they wish. You have done nothing that cannot be changed and they are free to do or not do as they see fit. They are trying to pawn off their responsibility on you and if there is no contracted obligation in place, then I would send them a registered/certified letter spelling out things like “industry standard tools” and “trade custom across the Internet”, etc., etc., and they will get the message that they have no case and are totally on their own.
Best regards,
Ron Lindeboom