I have dealt with a similar issue in the past. The key is to have your week start on Thursday, since that is the day of the new data. To solve my issue, I created the following Boolean calculated field and filtered for TRUE to exclude incomplete weeks. Each Thursday, you should get a new week of data.
[Your Date Field] <= DATEADD('week',-1, DATETRUNC('week',today(), 'thursday'))
This essentially checks your date field to make sure it is less than or equal to last week, with Thursday being the first day of each week.
So if your week resets on SUNDAY, that means you need to change your formula only when the day is Friday and Saturday, correct?
You could use an IF or CASE statement with DATENAME('weekday',NOW()) to change the formula you used based on the weekday name.
You can even use DATENAME('hour',NOW())) to confirm it's past noon on Thursday, too.
Which portion in the formula would I need to change?
you wouldn't need the entire ELSE clause. You only need the portion I provided above. Also, it appears that you're using a parameter here? You wouldn't need a parameter in the method I showed, you would use the date field of interest from your data.