I don't have any information on Anny. Kurc, Kurz and Kurtz are all different surnames from Kuruc-unless of course someone just happened to have left off a letter. Personally I have not had any ancestors change their name to Kurtz and found that these surnames were different from my research. Thus, I did not keep much in the way of records on these surnames.
My suggestion is that you put in the Kurc in the ellis island site. Then when the list comes up click on Close matches only. You could also try this for Kur but you'll come up with many more matches. Be sure to put gender and nationality in so that you can narrow down the choices.