Immigrants pay taxes. I would worry more about the broader effects of globalization as a whole than I would about immigrants remitted part of their paycheck back to their home country. And dollars aren't what makes the American economy strong -- it's goods and services we get in exchange for them, in the form of imports and (as one example) immigrant labor.

Before you come tell me that immigration is a net drain on the American economy, you should understand the dominant view in the field is that this is false. You will need to provide some evidence that what you are saying is true, not just a made up rationale.