1) Keep internal company traffic hidden. 2) Expose REST/SOAP/anything suitable here, to the MVC app. 3) That MVC app may be server side, client side, mobile, whtever. But it only consume "public" API. 4) Build middle man serivce that will handle requests from MVC app, and be able to talk to other parts of corporate infra.
That way, You and team in india have total freedom in designing for Your needs. MVC app can be run from Internet (and not behind some vpn, or something similar). Team in india do not know a single thing about internals of other systems (and You need not know about internals of MVC). Etc.
As a bonus You will have ready architecture for adding different clients (like mobile apps) in the future.