They point to strong similarities in the texture and composition of the debris found in the ice cores and that found in the granite.I imagine the spherules described in the article are extremely unstable under normal earth-surface conditions, but the long deep freeze of Antarctica has permitted the material to be preserved. This is not the first time spherules have been linked to meteors and meteorites, but the article states, "The spherules could potentially provide a signature to look for evidence of "airbursts" in the geological record."
However, the sites are more than 2,900km apart. For cosmic debris to be spread over such a wide area, the researchers propose that an airburst is the most likely explanation.
They estimate that it could have been caused by an object weighing 100,000 tonnes.
Antarctica is a meteoritic treasure trove. Here's the Antarctica Meteorite Newsletter, which appears to come out in Feb.-March and August-Sept. each year since 1978, and offers preliminary notes on recent finds. A more general overview is here, along with an amusing anecdote from the person who discovered the Allan Nunatak meteorite field... and didn't recognize it. It wasn't until a quarter century later that it was recognized for what it was: the greatest meteorite field on the planet.