I'm using a mac and I did see a post where someone was asking this same question - the answer was open your return, go to File, click on Check on E-File Status and in there it will tell you. I did this and there isn't a date. I'm using a mac.
Have you received an email from TurboTax saying that your return was accepted or rejected?
Please click How do I check my e-file status? to watch a brief video.
I did but I deleted the email. And yes, I checked my deleted folder. Since then I figured out a work around.
The only way I was able to find out is if you print out your return it has a date on the last page. I was just wanting to be able to see it in the software application.