My wife has a business in Italy, your form insisted we list the state. So I gave up and chose NJ and will have to correct the forms with a pen. Can you fix it?

If she has her own self-employment business, you will need to upgrade to the Self-Employment version.  When you first enter her name and address for her business, you can choose to indicate that her business has a foreign address. See screen shot below.

In TurboTax Business you can check a box that it is a foreign address.  See the screen shot below.

She is not self employed.  She is a partner in a business

I added a screen shot from TurboTax Business.