This refers to Moodle 3.10 from August 2021 onwards
Once you have set up a Turnitin Assignment you need to edit it afterwards to change the dates.
See How to create a Turnitin assignment drop box
There are 'Edit' icons (pencil icon) next to each of the editable settings.
Click a 'Pencil' icon to edit the date.
Edit the date using the dropdowns
Click away from the date elsewhere on the page and it will save automatically.
Known issue in Chrome and Firefox
On some screens, in Chrome and Firefox, the arrows required to edit the dates are superimposed over the dates. It is still possible to click on them and amend the date.