If you were telecommuting, you earned $0 in California. California only taxes you if you are physically working in California.
If the situation were reverse (living in California, but telecommuting to NYC company), New York would tax you as if you were physically working in New York, and they aggressively enforce that position.
You can delete the California return, if you did not live or work in California at all during the year. However, if California tax was withheld, they you will mark "no" in that box you mention, because you will file a $0 California return to get back all of the CA tax withheld from your income.
You will always pay NY tax, because your resident state will tax all of your income.
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