Say no and see what happens.
As far as I know, this mainly is required so that turbotax can offer you the refund transfer option (pay your fees from your refund for an extra service fee), refund advance (get part of your refund in 3 days on a debit card) and probably to offer you the option of a tax-deductible IRA to save money if are are eligible and don't already have one. It might also be required for certain kinds of customer support help, although if you end up needing that kind of help, you can change your permissions at that time.