From the list of documents required by the Indo Consulate, the former (old) contract is one of the items which you need to submit to the Indo Consulate.
So HinHinMa has to get hold of the "old" contract from the agent if the agent didn't return her a copy at the time the Indo DH was first employed.
Yes, your own copy of the "old" Indo DH contract will do.
I think the Indo Consulate want a copy for reference only, so that they don't need to search their own records, and so that they know who the "old" agent was. Your copy is the same as the Indo DH's own copy and the agency's copy.
The "old" copy will be returned to you together with the set of "new" DH contract.