Monies that already have been taxed at source ( US ) is your money . If this monies were to earn interest or other income in the USA , it would be deemed US sourced income and therefore taxable by the USA. The same monies earning foreign income is foreign sourced and hence not taxable to the USA , in your particular case. If this money was used to own shares in an Indian company, the dividend thereof may or may not be taxable depending on the source character ---- a purely Indian entity, not listed in the USA, probably would be Indian sourced, while a publicly traded Indian entity and listed in US stock exchange and doing business in the USA, may be considered at least partly US sourced. Gets complicated very quickly.
In your particular case, your interest income from an Indian bank is India sourced ( even when the deposit is held in US $ ). However, if the bank is a US bank or its branch ( depending on how it is registered/taxed in India ) may raise complications.
Namaste ji
