If you have some method of heating, you can add pasta and rice and beans and oats and sweet potatoes and lentils.
If people are really lacking these tools, I'd be happy to write a check to a New York charity that provides them.
(re your last point, I don't see how this family is going to take advantage of incremental assistance like that)
Whether that's true or not depends where you live. The US and Europe have developed different systems for egg production and storage.
Obviously none of the things I listed will form a complete diet, but if you are eating mostly take-out they are probably a superior substitute for some fraction of those take-out meals.
No, this isn't a technical problem. It's bigger than that.
Eating normal food, with some organics but not all, is reasonably affordable if you're willing to cook.
That takes longer, but results are better.
I don't know how people afford to eat out. It seems that unless you go Taco Bell (and there's no shame in that) two people is $25-50 per meal.