I question the use of a postcard as a means to bill me for a service. This seems to me to be a complete disregard for my privacy, not to mention tacky. Is it legal?
It depends on whether the debt has been assigned to a collection agency. Collection agencies -- an agency or person whom the original creditor uses to collect the debt --cannot use a postcard to try and collect a debt. However, no federal law prohibits the original creditor from doing so.
Some state laws might forbid such a practice. For example, creditors in California who regularly engage in debt collection cannot dun by postcard. To research your state's debtor protection laws, see Nolo's Legal Research area, where you'll find links to your state's laws.
If you remain bothered by the practice, stop doing business with the company -- and make sure you drop it a line explaining why. (Use a piece of stationery and put it in an envelope!)