Our CDs have ten day grace period and are all set to auto renew. We pay interest if the account is closed before interest is credited.

So if a CD is redeemed during the grace period, lets say on the 9th day, should we be paying 9 days of interest that is earning on the new term? Or is this not required because the CD was redeemed and never really went into the new term?

It's not a regulatory issue, but rather your policy. Does your CD contract address this. Legally, you don't owe them anything after the maturity date. The contract expired and your obligation to pay them ended on the maturity date.

If you're wanting to compare banks (we are $4.5B), we pay the interest IF it is automatically renewable. CD expires on 10/3/18, customer has until 10/13/18 to close, but the auto renew CD has already begun with a 10/3 date. The only thing our grace period does is allow the customer to close the CD without penalty.