If she does this and it is untrue, or at least not provable by her, that she was bitten by bugs at your hotel, you could sue her for defamation and potentially recover more from her than the $200 she is seeking, and you can make her aware that you will do this.
Also, to threaten to lie about someone to get money from them is extortion, a crime you could also report her to the police, if you believe her claims untrue.
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