Understanding Gratuity Eligibility for International Transfers
Presumably, your appointment/transfer order should detail the terms and conditions of your service benefits, compensation package, etc. Your case is unique, as you have served in various locations with different entities across different countries. Indian laws are applicable only within India, and I don't think you'll find relevant information in these legislations. Even if we assume that your entire service was in India, it is unlikely that you would be eligible for a gratuity payment under the Payment of Gratuity Act, as I believe your emoluments could easily exceed the limits set by the Act.
I suggest that instead of seeking opinions here, you should address this issue to them, discuss it with your HR contact who managed your career, or seek advice from colleagues who have left under similar circumstances. I have nothing specific to recommend regarding whether you should continue or quit based solely on the gratuity aspect. There are other crucial factors to consider as well. Perhaps the period (1.6.2011 to 1.9.2011?) during which you worked in India with an Indian-incorporated company could have some bearing on this issue, as I doubt whether you completed the qualifying service as per the PGA. Hopefully, some clarity will emerge when you inquire with your employers in India and the US.