The quick print buttons implement their own filtering. They are not aware of any current screen filtering.
1) You can set individual Row filters on all of the tables in the Quick Report.
2) You can add optional or mandatory criteria fields that the user can fill in when they run the report.
Note: You need to first save the report. Once you open the saved report you will then be able to set the criteria fields and row filters.
For more information please see: https://dbfront.com/quickreports