The purpose of carbon tarrifs is not to punish other countries.
The purpose of carbon tarrifs is to make foreign dirty-energy-intensive products less competitive, compared to less dirty-energy-intensive ones.
Because we already have a way of making domestic dirty-energy-intensive products less competitive. It works great. It's called a domestic carbon tax.
They remove the immediate complaint of "If we impose a local carbon tax on energy, foreign imports will outcompete us, because they don't have to pay it."