Dynamic Grid fed by Article Category - How to show published date

Edit the Grid item, and select Content > META > Dynamic > Article: Published.

Alternatively, select Content > META > Dynamic > Article: Meta, click on the pencil  icon, and — if you don't want to show the author — un-tick  Show author.

Regarding the date format — which you might want to change — please see https://yootheme.com/support/yootheme-pro/joomla/dynamic-content#date-format. Its syntax is that of the PHP Date function.