No, the 1095-C form just proves that you had health coverage. It would not affect your refund as long as you answered the Health Insurance questions accurately.
You don’t need your form 1095-C to file your tax return. TurboTax will ask you questions about your health coverage but your form 1095-C isn’t needed.
Just keep the form for your files.
If you’ve already filed and then receive it, it’s ok. You don’t need to amend your return.