While the player is free to choose her character's actions, nothing is stopping the others from doing the same. Her successfully flubbing does not stop anyone else from joining the conversation and just saying: "Do not listen to her, yes we have seen those people." They might be asked why she lied first, but that should not stop the interaction in itself.

So make sure she is not sent alone on errands. It seems her habits are known by the other PC-s, so this is a quite reasonable choice in-world too. The players should be able to implement this by themselves easily.

While the player is free to choose her character's actions, nothing is stopping the others from doing the same. Her successfully fibbing does not stop anyone else from joining the conversation and just saying: "Do not listen to her, yes we have seen those people." They might be asked why she lied first, but that should not stop the interaction in itself.

So make sure she is not sent alone on errands. It seems her habits are known by the other PC-s, so this is a quite reasonable choice in-world too. The players should be able to implement this by themselves easily.