Near the end of Episode 2 of Supergirl, Astra (a Kryptonian) says to Henshaw that humans have no weapons that can harm her, and then Henshaw surprises her by stabbing her with a blade of Kryptonite. She flies off in pain and then later has the following conversation with a Kryptonian scientist who is analyzing the blade:
Astra: Kryptonians are nearly indestructible on Earth. How could that blade hurt me?
Scientist: Unclear. I've never seen anything like it. It's definitely not from this planet. It seems to be emitting a specific radioactivity that's damaging to your cellular structure.
Astra: It's still making me sick. Get it away from me. Get it out of here.
I am not very familiar with the Superman canon, so I'd like to know why these two Kryptonians don't know what Kryptonite is.