I don't know if there is a name for it, but I see paraphrases put in quotes like this quite frequently in 19th century books. I personally think of it as similar to our current usage of the curled fingers while speaking to indicate a humorous (if not sarcastic) "quote-quote".
Incidentally, I have worked with quite a few 19th and early 20th century books from UK publishers that do indeed use double quotation marks. I think HarryT pointed out somewhere, somewhen, that the standard British usage of Single Quotes did not really take over until after World War I.
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