Final answer:
Katniss recognizes the Avox girl from an earlier encounter in the woods where she witnessed her capture by the Capitol.
Step-by-step explanation:
Katniss recognizes the Avox girl from an incident that occurred while she was hunting in the woods outside of District 12. Before the girl was captured and turned into an Avox, a punishment for rebellion against the Capitol, she and a young man ran into Katniss's view. However, they were being chased by Capitol hovercraft, and while Katniss watched from her hiding spot, the boy was killed and the girl was taken.
This traumatic event stuck with Katniss, which is why she later recognizes the girl when she sees her serving as an Avox in the Capitol during the Hunger Games. The Avox girl's presence is a stark reminder of the Capitol's oppressive regime and the consequences of defiance.