I put down my daughter as a dependent but said that her noncustodual parent claims her. His taxes got rejected. How do we fix this?

When you indicated that your daughter is being claimed by her father on his tax return she would be listed as a nondependent on your tax return but qualifying for other tax purposes. 

There is no way to reset the e-File system for this tax year, and her father will have to mail his tax return in this year.  

His tax return will be properly processed with her as a dependent; it just cannot be e-Filed.

If your return mistakenly shows her as a dependent, you will need to amend your return.  To amend your return, wait until you receive your refund, log back into TurboTax, and select the option "I need to amend my 2019 tax return."   Your amended return will need to be mailed in for processing and may require the return of some of the refund.  

You can find more detailed instructions on that process here: How to amend a tax return in TurboTax.