If a donor calls and says that they have a paid grant suddenly showing up that they don't know about and it does not appear to be in FIMS, it is most likely because of the following situation:
A grant was approved and paid last year, however the grantee calls and has lost the check. The check is voided and reissued in the current year. In Tools > System Utilities > DonorCentral > DonorCentral Options, selection System in the Section frame. If the Paid_Grants_Fiscal_Year setting for is set to Check_Date the grant will show up looking like a grant paid in the current year when in fact it was a previous year grant with a new check just re-issued.