Peeta saves Katniss when she says she recognizes an Avox by saying she looks like a girl they used to know.
Katniss, Peeta, Haymitch, Cinna and Effie are having a strategy session at the dinner table when they are waited on by a girl Katniss recognizes. Before she realizes it, she has told the girl that she knows her.
Effie says there is no way she could know the girl, because she is an Avox. As punishment for some severe, usually political, offense, the tongue is cut out and the person becomes a Capitol slave.
For Katniss to recognize such a person would be very dangerous. Katniss actually saw her when she was hunting in the Seam, and she was running away. This information would get Katniss in a lot of trouble if it was revealed. Knowing this, Peeta jumps in.
Peeta snaps his fingers. “Delly Cartwright. That’s who it is. I kept thinking she looked familiar as well. Then I realized she is a dead ringer for Delly Cartwright.” (ch 6, p. 78)
Katniss realizes that Peeta is rescuing her, and agrees. Everyone at the table relaxes. Later, Haymitch asks for an explanation. He knows that Peeta covered for Katniss, and they both lied. Katniss does not tell him. She is annoyed at being once again in Peeta’s debt.
The incident with the Avox demonstrates how even something as simple as dinner can be dangerous in the Capitol. If anyone suspected that Katniss knew the Avox there would be trouble.
Since Katniss said that she knew the Avox she almost got into huge trouble because knowing or associating with one could result in grave consequences even if she is a victor. Peeta rescues her by saying she reminds them of a girl back in District 12 and the atmosphere at the table relaxes, yet Katniss is annoyed that Peeta saved her again and she feels like she is in his debt one more.