The NICS background check system is administered by the FBI, not the ATF. If the background check is a proceed, the law requires the information to be deleted within 24 hours.
The ATF can request specific 4473's in conjunction with a trace, but they are forbidden from maintaining any sort of database of 4473's in general.
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Sometimes it’s nice not to destroy the world for a change.
--Randall Munroe
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