When Oliver, Barry of Earth-1 and Supergirl of Earth-38 (the heroes of their respective shows) face off against their evil counterparts from Earth-X
and Earth-1 (in Barry's case with his opposite being the Earth-1 Reverse Flash)
Overgirl scoffs at the ridiculousness of Oliver aiming an arrow at her.
She is understandably quite shocked (as is Supergirl for that matter) when it turns out to be an arrow made out of kryptonite.
Oliver answers Kara's question as to why he has it:
"In case an evil you ever showed up!"
When she showed up during the previous crossover, Kara had been mind-controlled, so it is not a bad idea to have a contingency plan in place in case something like that happened again.
He doesn't say anything as to how he has it, though.
My question therefore is:
How did Oliver Queen of Earth-1
- learn of the existence of kryptonite in the first place, and of the fact that it is harmful to Kryptonians (something that by the pilot episode of Supergirl Kara herself didn't know [although it has become an Earth-38 idiom for crippling weakness within 2 years! (iirc Lena asks Kara what her Kryptonite is at some point)])
- procure enough of it to craft an arrowhead. As far as we know there are no Kryptonians on Earth-1, therefore debris from Krypton should not have been dragged across the galaxy (or galaxies depending on where Krypton is in this continuity) to crash there. We know from Supergirl - 3x04 - The Faithful that Krypton-38 did send probes with soil samples to other worlds, so maybe Krypton-1 did that, too?