You can find the quoted date if you navigate to the quote section of the deal card.
To view the enhancement:
Navigate to Pipelines
Click on the Deal Card for an extended view of the deal card
Click on the Quotes to open the quote
Click on more options
You will find the Quoted Date
By default, it will show the current date which you can change manually
Once you submit it cannot be changed unless it’s manually done from your end
Note: The Quoted Date will not be visible if the card is marked won/lost/close
If you download the deal card report of the selected Pipeline, you will have a different column for the quoted date where you will have the quoted date and time.