You can delete your state return by following these instructions.
Note: If you've already paid your TurboTax state fees or registered your free version with your state return attached, you can't delete your state return.
If you’ve already paid your state fees, you can’t delete your return, but you can start over by selecting Start Over next to your state return on the Status of your state returns screen.
Here's how to clear (delete) a state return in the TurboTax for Windows CD/Download software:
If you want to start a new state return, select the Step-by-Step icon, and then select the State Taxes tab.
You did just tell the Forum Q&A system you are using the "Online" TurboTax software?
Hope you aren't actually using desktop software.
How do you uninstall the state, so that it does not keep appearing?
Please see this Turbo Tax FAQ on how to delete your state return.
How do I delete my state return in TurboTax Online?
How do I clear my state return in the TurboTax for Windows software?