I wondered that also, but it doesn't seem logical that Qantas would cancel a perfectly legitimate booking that had already been updated instead of just pushing a button to issue an e-ticket.
It might seem logical to the Qantas staff trying to deal with your situation and not able to modify the original ticket due to restrictions with who is able to modify a ticket issued by a TA.
Last reply from Qantas (24 Feb) for the record:
"We have reviewed your case for [the original booking] and can confirm that the amount of INR 980.00, which had been deducted for voluntary change, will be reversed back as no documents were issued. Additionally, we can see that you have not utilised your tickets. Should you wish to discuss this booking further, please contact your Travel Agent for assistance.
Perhaps the airport staff were not even able to cancel the ticket and expected that you would contact the issuing TA for them to cancel and refund the remaining value of the ticket? Again, if that is the case, and it was not clearly communicated, then that is very poor communication from the Qantas staff you were dealing with. That reply from Qantas does suggest to me that the original ticket has not been cancelled and refunded, but may still be able to be cancelled and refunded based on the evidence you have regarding the process.
However, for [the new booking], we can see that this booking was created directly on the website. As you have successfully flown on these tickets, we are unable to process a refund."
It's not clear to me from the above that Qantas has issued a credit for the part of the original booking not utilised. I've reached out to the organiser, as I don't have a direct line to the TA.
It does sound like they have not yet issued a credit for the unused return ticket. I suggest you contact the issuing TA and ask them to seek the refund and pass it on to you. Hopefully it will be sufficient to come close to the amount you were charged for the new flight booking.
Again, I am in no way defending Qantas in this matter, just providing some ideas about what may have transpired from Qantas' perspective. If this is correct, then I will say again that it is very poor communication from Qantas' staff both on the original call implying that they could make the change for you, and at the airport for making a new booking without full explanation as to why and how to seek a refund from the original TA.
And this will be even more complicated because you did not pay the TA for the original booking, so they may be unwilling to forward the refunded value to you and may insist that it can only be sent to the person/company originally requesting their services.
I feel for you - its is likely going to a lot of work and quite difficult chasing up all the parties involved. As other have suggested, easiest way would be if the CC provider accepts a charge-back request, but it seems from Qantas' reply that as far as they are concerned you purchased a new ticket and flew on that new ticket. In their mind there still an unused return ticket with flexible terms that may hold some value, but the only way you can access that value is likely to be for the original TA to request a refund of unused value from Qantas.