Should I tell the recruiter I was fired and not laid off?

I applied to work with a staffing company to find a job. I was fired from one of my jobs but I told her I was laid off. The issue is that they will conduct a reference check and find out I'm not eligible for rehire. Should I call the recruiter and let her know that I was let go and explain what happened? Or should I just leave it alone?

usa jobs
usa jobs resume
usa hotel jobs
usajobs
usa jobs federal government
usa job in ksa
usa jobs
usa jobs login
usa jobs gov
usajobs.gov
www.usajobs.gov
usajobs.com
usajobs
usajobs.gov official