As a permanent resident, and presumably, a US citizen, you will file taxes in both countries. The US charges tax due to citizenship, whereas Canada charges tax based on residency.
The company can pay you as a contractor. You will be reporting foreign income including the exchange. You will also be able to report the tax retained by the US company as a deduction.
You will need a copy of whatever slip the company deems appropriate. You will have to ask the company how they normally report this type of income. To them, it is not foreign income, so it may be on a 1099 or any other appropriate form. In Canada it is simply foreign income reported on your personal income tax.
