It is a transfer of funds subject to the recordkeeping rules for transfers of $3,000 and up. The "cash" was simply a contrivance on the part of the bank to facilitate the transfer.
I'm not understanding why "privacy" came into this. Did the parents not want the daughter to know they transfered the $20,500? What privacy issues are there? If you completed a transaction authorized by the customer, there are no privacy issues, and you made a simple transaction much more complex.
You will probably need to write some sort of memo to some sort of file to explain why this virtual "cash" transaction is not being reported on a CTR in case the question comes up in an audit or an exam.
Beyond that, I think you need to examine why you believe you needed to conduct the transaction in the manner in which you did.
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CRCM,CAMS
Regulations are a poor substitute for ethics.
Just sayin'