The Lord of the Rings was first published in 1954. According to one of the sources in my previous post, die-hard fans have been writing in Quenya since the 1970s. It is perfectly possible for your parents to have been aware of the constructed language at the time of your birth in 1998, 44 years after the publication of the books.
Forchta in biuonga quamon ouer mi, in bethecoda mi thuisternussi. In ic quad: "uuie sal geuan mi fetheron also duuon, in ic fliugon sal in raston sal?"