What would be the process for imposing a tax on remittances sent from the United States?

You would have to tax it on a state-wide level. It is already in effect in one state: Oklahoma. The remittance tax in OK is $5 for remittances up to $500 and 1% of the total amount being remitted over $500.

The financial regulator of the state can make this tax deduction mandatory on a state level, so that all banking and non-banking financial institutions that are licensed and/or operating in the state, would have to adhere to it.