Sorry to hear that has happened, seen similar things a few times over the years. FWIW -- my advice is based on having worked with India firms and individual freelancers since 1998 in various capacities, overwhelmingly positive experiences but not all.
In general you got it removed quickly, which is critical and really awesome. I'd push the company in India to refund some of your fees (or not bill for anything outstanding) and affirm that they are dealing with the situation and have them guarantee (in writing) that this will not reoccur and that all code has been removed from their and their employees equipment. Reputable India contracting firms do not want the bad look either so they generally will deal with it quickly and make sure it doesn't happen again.
Personally, I'd be really cautious on going super public and shaming them at this point because you have to understand that your chances of recourse with an India based company and individual are nearly zero. Creating a lot of noise posting their names and stuff could cause them to retaliate and put the code up for good in many places not just GitHub. GitHub you'd have a good chance of a DMCA type takedown since it is your property, but they'll just post it in 30 other places that won't recognize such requests.
You also have to understand the courts in India are SLOW and won't favor a western company over one of their companies/citizens, with a few exceptions. If you were a large corp, e.g. GE, Fiserv, Microsoft etc then things are different -- plus most of those have in Country subsidiaries to try and control IP etc. If you took them to court in the US (based on how your contract is setup) the US courts may rule in your favor but they have no way to enforce a ruling against them overseas, so great you get a judgement but your code is still published.
If they publish again to GitHub, absolutely send a takedown request and document the details. Otherwise, my 2 cents is to just move on and be thankful you got it down quickly.