No shit?
Can you just throw it into space?
We should definitely try doing that for all our waste on earth as well, why didn’t anybody think of that ^^ although on the moon you probably wouldn’t need a rocket to launch it into space i guess
The escape velocity of the moon is over 2 km/s, so you would definitely need a rocket to get stuff into space from the moon. And even then it’s still just in orbit around the Earth, just like the moon is. With the risk of it being disturbed and coming back down some time in the future. It would really suck to be on the surface of the moon and be killed by a meteor of shit coming down.
As for why we don’t do that on Earth and nobody ever having thought of that, I hope you are joking.
Once working colonies become a thing, any organic matter will be worth its weight in uranium.