Just bury it out back, we'll clean it up later just like we did in Hanford. No problemo https://en.wikipedia.org/wiki/Hanford_Site.

More seriously, we can afford to have a small amount of nuclear waste there, but we need to plan for it better than we have previously. First, document where it is and what it contains. Second, I don't know.

Or Runit Island: https://en.wikipedia.org/wiki/Runit_Island

Yep, Hanford Site was/is an epic disaster.

The correct response is reprocessing. Most of the "waste" generated by power reactors is actually still usable as fuel. It also eliminates the really long-lived stuff, so that the small amount of leftover waste only has to be kept stored for a much more manageable 500-1000 years.

Fun fact: right across from the Hanford Site is a massive Conagra plantation. Source: visited Hanford Site, looked up the company associated with the plantation across the road.

That's so when the Martian Congressional Republic eventually decides to declare war on Earth, they'll be weakened from the get-go. It's called playing the long game...

How does pollution work exactly in an environment that's already hostile to life as we know it?

It adds one more element to overcome when we decide we would like to live there.

It's not like radiation is a non-existent problem to begin with on a planet that does not have enough atmosphere.