Why do you want to remove it?
Unfortunately, I don't know of any way to leave it off, short of using the desktop program and forms mode to override it. Overrides can't be e-filed and they void the accuracy guarantee. And I don't know about NY, but if you are eligible for federal EIC and leave it off your return, they will automatically add it for you. If you find it is not automatic on the NY return you can try and skip it; for example, if the program says something like "You appear to be eligible for NY EIC, let's double-check your qualifications" maybe you can skip it. But if it automatically pulls it from federal, I think you aren't going to get around it.
I don't study other software. But the problem you will have, I think, is that the demand for guranteed accurate returns and maximum refunds is going to mean that every company will automatically include EIC if you qualify, and as I said, New York may add it for you if you try and leave it off.