woking remotely for a less than a month in another state

@NCPERSON1 

Q. If I work in NC for 3 weeks remotely from my son's home this coming April, but live and work in IA with my employer in IA, do I owe NC income tax on that income and have to file an NC tax return?

A. Yes, but "nobody" does. See http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/  If you live in a state without an income tax (e.g. FL or TX), it’s more likely you should file in the work states. You can't use the "it all comes out even" rationale for not filing.

The issue isn't how much time you spent in NC; the issue is how much income you earned there.

By law, income from work you actually (physically) perform in North Carolina is taxable by North Carolina.  You must file a non-resident NC tax return if your federal gross income exceeds NC's filing threshold.  You can see those threshold amounts here:

https://www.ncdor.gov/taxes-forms/individual-income-tax/individual-income-filing-requirements#Filing

If you must file in NC, your home state of IA will credit you for all or part of the taxes you pay to NC, so in effect you won't be double-taxed.  In order for TT to calculate the credit, you must complete the non-resident state tax return before you do your home state return.  (Your home state of IA can tax ALL your income, including what you earn in NC.)