I'm interested in this as well. I did not leave on the best of terms with my previous employer, and I'm slightly worried that they may give out incorrect information. Long story short, Indian employers generally require you to sign contracts saying you will work for them for a set period (2 years in my case) and there's a hefty penalty (=~ the total amount of post-tax money I was making over the 2 year period) if I leave.
I had to leave the company for personal reasons after 18 months and after prolonged discussions with HR, they agreed to let the matter slide, but wouldn't officially give me an experience letter for the period I worked there. I was moving to the US at that point and I did not think that not having an experience letter would make a difference.
I have a couple of internal contacts (who are still with the company and reachable via official email) that are happy to speak about my tenure, but I'm worried that the agency performing the background checks will contact the HR department directly. Is there a way to give them a contact to talk to?