So two things are noted, one that it involves a woman and an incident in high school and the other that this has been referred to the FBI. Since statute of limitations will have run out on any high school crime short of murder, how about this for a hypothesis:
The lady made her intentions to go forward with a harmful story known to Kavanaugh, sometime after he was on the DC circuit. Knowing that the $10k bank withdrawal limits are what got Hastert, Kavanaugh uses his credit card and "baseball tickets" to effectively launder payoff money to the woman.
Somehow this surfaces and thus the crime referred to the FBI would be financial/blackmail/bribe related. This would be a relatively recent crime, on inside it's own statute of limitations.
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