According to the episode it was the U5 form[0]. Banks use the form as one of the employment references.
[0] http://www.finra.org/industry/terminate-individuals-registra...
[0] http://www.finra.org/industry/terminate-individuals-registra...
Every time she tries to get a job anywhere, that form will be checked by her potential employer?
Unfortunately, company insiders may see little difference in a "misbehaving" employee, regardless if it's in the public good and/or for personal gain, because limiting the threat of public exposure is often the paramount priority in the short-term, which may ultimately go against long-term business and customer relationships. And an "untrustworthy" bank is unlikely to survive on it's own for very long.
Most jobs involve some referencing, talking to previous employers etc. I guess this is different because the banks all agree to abide by the black mark.