The first version she pitches is the “rational” one. Lopez says that since Hank moved her body, he was the one who cut out her tongue and left it by her as Hank has a bit of a psychopathic streak, even if he’s just playing the mine grunt doing what he’s told. This served as a message about not messing with the mine. Then, the women of the village find the tongue when Annie K’s body is found, and as an act of reverence, they keep the tongue on ice for years, freezing it somewhere. Then, once they realize the scientists killed her, they bring the tongue to the raid and leave it there, connecting the killings to Annie K, even if it took forever for Danvers and others to figure out who the scientists were actually killed by, and that they killed Annie K in the first place.
The other explanation is…ghosts. That the tongue disappeared into the ether, and then the ghost of Annie K comes with the women and leave it there. Here’s Lopez:
“It is Annie who comes with the women into the station, like she’s awake. Clark says, “I knew she was coming.” Annie does visit the station with the women, and leaves her own tongue, because she knows this is how it starts — that she can finally tell her story.”