If we had solid immigration programs that gave an easier route to permanent residency and didn't make work visa applicants indentured to their employer foreign engineers would be demanding higher salaries and the wage gape would reduce. The current system makes it easy to kick out foreigners so they know their savings are going back to their home country so they don't care as much. Also, they can't play the job market because their visa status is largely tied to their employer.
If we introduced some simple policy reform (and overhauled the H-1 program) the whole foreigners cutting wages issue would go away.