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One way you could approach this is to create a dynamic filter based on whether today is Friday or not. First we would need a field that identifies if a delivery date is part of the current week or part of last week. We can do that with the DATEDIFF function.
This calculates the number of "weeks" between today and all your delivery dates. It will return 0 for days that are part of the same week as today, and 1 for days that were in the previous week. If we call that calculation "Weeks Difference" then we can create a second calculation that filters data based on whether it is Friday or not.
IF DATENAME('weekday',Today()) = "Friday"
THEN [Weeks Difference] = 1
ELSE [Weeks Difference] = 0
This calculation evaluates differently based on if it's Friday or not, but we will always want to keep the days that evaluate to TRUE. Place this new calculation on the filters shelf, keep TRUE, and then you should have the basis from which you can build your appropriately filtered view!
Hope this helps.