As Christians, we can and should be concerned about human labor exploitation, especially when the situation involves predatory behavior.
Allowing immigrants from a relatively poor country into a relatively wealthy country does not inherently exploit the situation of the poor. To know whether such behavior is happening, we need to assess relevant information, and we don't always have what we need. If an immigrant travels across the border to perform work, he is doing so because he is choosing his best known available opportunity for work. If he were restricted to his own country, he would have fewer options. It is an unjust situation for this poor person to be restricted from voluntarily offering his labor to a willing employer.
Some object that this situation is suboptimal, and they would be right. It would be nice if everybody had the skills to perform high-value labor and the employers had the profit margins to pay top-dollar wages. But the world we live in is one of limited knowledge that increases through discovery, and it is up to us to discover how to best cooperate and exchange within the parameters of peaceful, voluntary work.
Lastly, we ought to be very careful to not assume that we know what is better for the lives of immigrants than they do for themselves.
This question is from Faith Seeking Freedom: Updated & Expanded, available in paperback, PDF, and Kindle.