I had written to the Grievance office of the passport seva as below:
"Dear Sir/Madam, I have recently applied for Global entry program (GEP) background verification. My file number is XXXX. I have to congratulate you on the speediness with which I was able to book an appointment online,visit the PSK and have the police verification all done within and week and utmost professionalism. Thank you for setting up this wonderful process. Now as I await for further verification by relevant authorities ,I am wondering if you could share the following information, 1.What are the next steps taken in the verification process? 2.How long will it take for the process to be completed and results submitted to the US authorities? 3.Have there been any approvals so far? Appreciate any information, kind regards"

Had a reply promptly within a day or two as below:
"Dear Sir/Madam, It is informed that, first local police verification will be done. then Ministry of Home Affairs, New Delhi and Ministry of Finance, New Delhi have to collect reports from various agencies, the received reports should be scrutinize and compile them and have to send a clear report to this office, this process may take few months, then only this office can take further necessary action under intimation to you as early as possible. It is also informed to you that the fees paid by you is valid for 5 years. Your Sincerely, Public Grievance Cell(GO Role-1), Regional Passport Office, Hyderabad."

And other than the above, I have the standard status message:

"GEP Verification Process has been initiated on your application. Once inputs from all the concerned Government Authorities are received, the Report will be shared with U.S. Customs and Border Protection (CBP). No queries would be entertained in relation to your GEP application status at the Passport Offices and PSP Call Centre. You may contact CBP for further updates on the processing of your GEP application."