How do I cite this old postcard?
Forget for a moment APA style and ask what a citation is: A way for a reader to find the source you used so that they can check themselves. APA and other styles provide sort of a general format to do this, but the essence and end-all is not that you slavishly follow the style, but that you follow the spirit of making a resource retrievable with the information you provide.

In the current context, that means that whether or not you provide the author's name doesn't really matter: Knowing the author doesn't help anyone find the postcard. So just go with what is suggested on the website to cite the document.