Social Security numbers as tattoos were real stories (embellished or not) from pre war (1938) https://trove.nla.gov.au/newspaper/article/58807906

and post war (1954) https://trove.nla.gov.au/newspaper/article/28664659

The Hollywood style reality of the holocaust most Western people follow didn't come around until the 80's. I don't think people would link the two ideas post war.