Nobody has shown that TurboTax is doing an incorrect calculation on Form 8880, so it's likely that the difference is due to some of the entries that go on this form, all of which derive from user entries. Assuming that the paid preparer is doing everything correctly, this implies that you have not accurately duplicated all entries that went into the preparation of the tax return prepared by the paid preparer or the difference is in some other aspect of the tax return that is being determined differently and is resulting in a different AGI, different amount of taxable income or a different amount of certain other tax credits. You need to compare all other aspects of the tax return before comparing Forms 8880.
The only items that go directly on Form 8880 that affect the determination of the credit are student status and the amounts of any recent distributions made by you or your spouse that reduce the amount of new contributions that go into the calculation of the credit. If your paid preparer was unaware of these and did not make the corresponding entries, it's possible that the Form 8880 produced the the paid preparer is incorrect.
