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They say it's a smaller share, which doesn't necessarily mean fewer women, depending on what is counted as "work".

It could be (I'm just guessing here), that the type of work that men do has been "legalized" (and hence counted) to a much greater extent than the type of work that women predominantly do.

Most people in India work in the informal sector and are not counted.

That also means these most people won’t have acceptable work conditions and other employee rights that the formal sector has.

Or they work on farms, or they build crafts as craftsmen/craftswomen in their own workshops, etc. Definition is very broad.

http://www.bbc.com/news/world-asia-india-39945473

"Improved stability in family income can be understood as a disincentive for female household members to join the labour force"

I don't have data to back it up. But this simply is not correct. Social norms have changed over the last few decades and that alone means the percentage of working women have gone up. Very few of the women of my age group are housewives, which was the default a few decades back.