The income is taxable in India as it is paid by an Indian employer. You will not get the refund of the taxes withheld when you file your tax return. This is a reciprocal arrangement. In the U.S. you can't pay wages to a non-resident without "backup withholding".
For this read IRS Publication 901: Tax Treaties --Personal Services Income, India
Internal Revenue Service
So you should have full account of your income and taxes paid in India including the dates. May be you can get Form 16 (equivalent of W2) or if the company does not want to give you Form 16 now, then get a statement of income and tax deducted from the employer. When you file your tax return in the U.S., you will get credit for taxes paid in India.