In your script that currently finds the person you just need to add an extra find criteria.
Enter Find Mode // in your current script
Your Name find script step is here however you have set the field
Set Field [ YourTable::YourDateField; Get ( CurrentDate ) - 7 & "..." & Get ( CurrentDate )]
Perform Find [no pause] //this should already be in your script
There are many other approaches as well depending on what you mean by the past week e.g. only the last 7 days or if you are running the script on a Monday and you want everything from the past Saturday (2 days ago) to the previous Sunday, or it is Thursday (or Monday) and you want everything back to Sunday (the last 5 days or 2 days). Each option requires different scripting but could all be done in one script where the user can be prompted which time period to pick.