How can I talk to a representative? Not an automated script, an actual representative?

The IRS sends it to the address on your tax return.  TT would not know anything else about it.

Bit what do you mean by "routing address"?

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@ utcaco wrote:
I'm pretty certain my tax refund was sent to entirely the wrong routing address. The IRS says they sent it out

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Are you referring to direct deposit numbers?   If so, here are some possibilities for routing and account numbers you do not recognize.  The first one is the most common.

Did you happen to pay any TurboTax fees out of your Federal refund?  If so, then the IRS sends the deposit to a temporary bank account in your name at a third-party bank, where the fees are subtracted.  Then that bank sends the rest to your bank account (or card) in a second direct deposit.   That process is administered by a company SBTPG (aka TPG or Tax Products Group.)   If you used that service to pay your TurboTax fees, we can tell you how to check on your refund using the SBPTG refund lookup tool at their website.

Or did you happen to choose to get your refund into a Credit Karma Money Spend account and Credit Karma Visa Debit Card?   If so, that's administered by MVB Bank.

Or do you have a brokerage account that it might have gone to?  They use an underlying bank routing and account number to receive deposits into cash accounts.

Or are you saying you think you mistyped the routing number?