What if they don't, are all exports going to be more expensive now in comparison with countries without this tax?

What if they claim to have a pollution tax but are lying at the state level?

It gets really complicated really fast.

If pollution is taxed at the source how do you calculate how much of a refund to give when exporting? Probably no one can even calculate that for you.

And not giving a refund would destroy exports which is an obvious problem.