Step 1: Clarify the Inquiry.
The query seeks identification of the inaugural Indian pair to secure a medal at the Asian Table Tennis Championships.
Step 2: Evaluate Each Choice.
- Choice A: Manika Batra and Sathiyan Gnanasekaran, while skilled, did not achieve this specific accomplishment. - Choice B: Sreeja Akula and Mouma Das, notable players, did not secure the initial medal at the Asian Table Tennis Championships. - Choice C: Neha Aggarwal and Ankita Das, despite successful careers, were not involved in this historic achievement. - Choice D: Madhurka Patkar and Archana Kamath also did not win the first medal. - Choice E: Accurate. Ayhika Mukherjee and Sutirtha Mukherjee earned India's first medal at the Asian Table Tennis Championships.
Step 3: Determine the Outcome.
The correct response is Ayhika Mukherjee and Sutirtha Mukherjee.
Final Determination: \[\boxed{\text{E}}\]