You don’t tell them what you earned. Your W-2 tells them what you earned, and it tells them how much FICA was withheld. The EITC is a FICA rebate.
http://www.payroll-taxes.com/articles/earned-income-credit-infromation
I know someone who did this and I’m pretty sure it is a bull shit scam based on what he told me.....
“The EIC may lead to a refund even if no income tax was withheld or owed.”