The takeaway from the responses above is this:
OFAC prohbits you from doing business with any entity on the SDN list. It does not prescribe a course of action for how you avoid doing business with any of these entities.
So the answer to "Are we required to screen..." is "No"
The answer to "Should we screen" as Randy says is based on your risk assessment. Since wires are a higher risk transaction, Ed recommends as a wise risk mitigant. (I agree). So we would answer "Should we screen..." as yes.
You could choose not to because you trust that the originating bank screened their customer already...but suppose that they didn't or the originator wasn't a customer and the bank accepted a cash wire and someone missed a step...
My automated system screens the originator, the originating bank and any intermediaries in between because my risk tolerance non-existant.
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