Their detector measures mostly positively charged antimuons, and the electric field in a thunderstorm would tend to slow them down and reduce their energy--by of order 1GeV. This would cut down the rate considerably. High energy muons would make it without trouble, but fewer of the much more numerous lower energy ones would.
This is a clever measurement.
But.
I can't read the original paper yet, but Whitehorn pointed out that in a thunderstorm there's a gigantic updraft, so the density at high altitudes (10km and more) is a lot higher than before. That slows down muons too, and would likewise reduce the rates. I'm not sure how much.
Hariharan et al could well be right. There's a puzzle--we see anti-electrons from thunderstorms. That speaks of very large energies, which means very large accelerations, which means very large potential differences, and gigaVolt differences are about right.
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