They have to apply for replacement checks.

Filing the tax return will have nothing to do with getting the refundable credit, since the IRS will show they were given the funds. It's the funds, not the tax filing, that they want to pursue, to get the money. The Tax Return will show they already got the funds, because they did get the funds. There is no way the IRS knows that they lost the checks or simply refused to cash the checks, unless they file for replacements. That way, the IRS can investigate and confirm the checks were never cashed. None of that is triggered from the tax filing.