Some police officers have just figured out that the drugs are sent to town in boxes with some documents which come to the courthouse.

One of them says: The courthouse records filings are a great way to ship the drugs. DEA or ICE agents would just let it right on by.

Does "records filings" mean just documents? Boxes with records filings.

How to say "let it right on by" differently?
'Records filings' is not quite good grammar, but what they mean is the filing of the records, i.e. shipping the records to the storehouse.

Let it right on by = let is pass without stopping and examining it.
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Ok, so you think it means that these records are shipped to the storehouse from the court or the other way round?
I was not paying attention to the direction. Wherever the records are filed, that's the direction the drugs move, I presume. 'Filing' could mean formal submission to the courthouse officials or filing away in storage.
Ok, I think I understand.

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