On the transcriptions that have been proofed and posted online with the
image, I believe I've only seen the note, without quotation marks.
The one instance of quotation marks I've seen on the certs so far was the
example showing a nickname for the father as "Fint". Personally, I would have
entered the given name of the father just like that on the transcription,
including the quo. marks, but only if they were actually shown on the cert.
Janice