If you're on Tableau 10.3+, you have the Latest Date Preset filter option --
but only for Date / Datetime type Discrete (Blue) Pills. No luck with Strings.
So you may want to create a new calculated field like this:
DATETRUNC('week', [your_date_column] )
and set the Default Properties for this pill:
1) --> Date Format --> Custom:
YYYY - \WK ww
2) --> Sort --> Descending (Data Source Order).
3) --> Fiscal Year Start --> (Choose the Month).
With that in place, the Filter on Individual Dates and Times
would get the expected result.