Unfortunately, India has very conservative laws with respect to outwards flow of money and the typical money brokers can not do much. The laws have been liberalized quite a bit in the past few years, but sometimes the burden of proof is high.
Getting money out is possible, as long as
a) you can prove that you have paid taxes on this (then it does not matter it is in NRO or Resident account). Proof == CA Certificate
OR
you can prove that it is against funds that were brought in
b) it is within limits (200K max for a year I believe)
c) you are willing to invest a lot of time to make this happen
Although the rules are straightforward, the implementation varies from bank to bank, from bank manager to bank manager, and from bank clerk to bank clerk. That's why I said you might need to invest time to make it happen.
If it is a resident account, they will ask how come you have a resident account since you are not living there.
But to convert to a non-resident account they will say they need a bunch of documents.
These documents will require a visa, and many of them will say GC is not a visa. Also, if you show the GC, they will go back and ask why you did not convert the account so far.
Some of them will say they will take care of it, take all the paperwork, and reject the transfer a week down the line saying our head-office found some issue with the paperwork.
Only way I was able to make it work (using GC) was to sit on their head, keep procuring documents as requested, and not let go until the transfer was done. It sounds easy, but could take a week, so if you are in a hurry, good luck.
Again, things may not be as gloomy as my experience was specifically with one bank. However, start with the documentation list required for such transfers as listed on the bank site. When filling forms, be consistent. Do not write non-resident on a resident account, or vice versa. If you have any specific questions, feel free to post them here ... we have anyway started discussing the issue, so we might as well close it.
Last, depends on the quantum of funds being transferred, most of the currency shops in India can give you TCs worth 10K USD based on a declaration that you have not taken any more forex during that year. This can be done for each family member holding Indian passport - again I have seen implementation different from vendor to vendor. See if that works, but note that such transactions must be reported to customs on landing in US. Wire transfers are automatically reported so it is easier.
