What is the interest note on the bottom of the Federal tax refund check?

In some cases, the Feds are required to pay interest on refunds, depending on a number of factors like when you filed or paid, and it may be that. It can also be that you owed interest on some portion of tax that was underpaid or not paid on time, although you may have a net refund coming. For example, if you had to pay estimated payments every quarter, but didn't - the fact that you may have paid even more than you had to at a later time and have a refund coming, doesn't mean you don't owe interest on the payments you failed to make timely.