Do a on change microflow on the date selection. In the microflow check if the date is between the project date. You can use the addDays($delivertyDate, -2) to get the second date. To check a thursday you check this page to see what you have to use in the formatDateTime command to get the day (E).
[EDIT] It depends a bit on how you build your screens because with a nested dataview you can pass two parameters to a microflow. Otherwise you should use a reference to connect the two objects you need. You can do this with a custum new button that creates the object and set this reference. Then you could use this reference in the on change microflow to retrieve the other object.
You can also choose to use a dropdown (reference selector) and populate it with non-persistent objects from a microflow datasource. Not as pretty as a pop-up calendar, but on the upside, the user is only able to select dates which make sense (and improve the user experience IMO).
Isn't it possible to just calculate said date? The way you formulated it it seems to me that there is only 1 possible date? The thursday before the project delivery date.
If this is not the case I think Roalands suggestion will provide the best user experience (and will also be most logical for the end-user) Just give him a list with possible options which you should be able to define via a microflow