You don't have to have a working definition of a "gene" to answer that question, you have to have the ability to pick an answer out of a lineup. This is called "standardized testing" and is what a lot of western countries base their educational system on.

They aren't writing a paper where they have to explain it, they're responding to a question, so it's very easy for someone who has no knowledge, experience or understanding of science or biology to intuitively assume that "genetically modified tomato" means "tomato modified WITH genes" as opposed to tomato with MODIFIED genes. For someone whose best career option is working a broom, or filing forms at the sheriffs office, genes are a very closed and uninteresting book, but they are also humans, humans who don't like to say "I don't know what that is".