I would report it. Though, depending on regional dialects, I'm not sure whether or not "left-handed" is more natural than saying "with the right hand". I'm familiar with both ("write left-handed" and "write with the left hand").
I am a native speaker of American English, and I find it perfectly natural to say "with the left hand". I put that down, but was marked wrong. It is also perfectly natural to say "with my left hand", but "with the left hand" is good English and should have been accepted. Neither is more to be preferred than the other; it is the speaker's individual choice.
Native English speakers would probably never say "with left hand". It sounds grammatically incorrect. Whereas " with the left hand" sounds like a contrast to the right hand. So "I can't X left-handed" or "with my left hand" sounds the most natural. I'm an American native speaker.