1099-Q in Error?

Apparently the financial institution considers this as a distribution, and recontribution that was done so quickly, you never saw a check. 

This is not a taxable event. You can enter the 1099-Q and select 

"Yes,..." for Refund of Education Expenses

and 

"Yes,..." for "Were the refunded expenses recontributed to the tuition program?"

Enter the amount 

An alternative is to just not enter the 1099-Q into TurboTax.

You can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses,  to cover the distribution, or you put the money back into the 529 plan within 60 days.  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. You also cannot count expenses that were paid by tax free scholarships. You cannot double dip! 

References:

1. On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 
2. IRS Pub 970 states: “Generally, distributions are tax free if they aren't more than the beneficiary's AQEE for the year. Don't report tax-free distributions (including qualifying rollovers) on your tax return”.