If your return was accepted then TurboTax does not get any more information regarding your return/refund.

For Federal refund you can check the IRS website, Where’s My Refund.

https://www.irs.gov/refunds

If you have a State refund, you can check the status on yours State website.

How do I track my state refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...