score:12
Your extra bag, unfortunately, will not travel as the second passenger will never be boarded.
This is an almost universal security practice across all airlines and airports; except for fringe situations like charter aircraft, pleasure flights and some domestic airlines - none of which applies to you.
Now, how you can avoid this is if you have one flight from IAH - BOM return; because then the most significant carrier rule applies. This basically means that the baggage rules that apply for the majority of your journey, will apply throughout the journey - across all carriers, from the time of check-in until you collect your bags.
There are (as always with these things) a few caveats - mainly, who is the marketing carrier vs. the operating carrier. Therefore, it is best to check with your airline - as you may be entitled to additional considerations based on your itinerary.