[BroJoeK]

Moonman62: "We should assume these 'fossils' are of non-biological origin until there is stronger evidence otherwise."

Here is a photo, this article said they are about 1.6 inches high:

Stromatolite fossils have been found in many places from many different time periods, including the relatively recent past.

[Moonman62]

From your article:

The dating seems about right, said Abigail Allwood , a NASA astrobiologist who found the previous oldest fossil, from 3.48 billion years ago, in Australia. But Allwood said she is not completely convinced that what VanKranendonk’s team found once was alive. She said the evidence wasn’t conclusive enough that it was life and not a geologic quirk.

FYI: Stromatolites are still being formed in some parts of the world.