I would simply do the following to backup all new files from 7 days ago
tar --newer $(date -d'7 days ago' +"%d-%b") -zcf thisweek.tgz .
note you can also replace '7 days ago' with anything that suits your need
Can be : date -d'yesterday' +"%d-%b"
Or even : date -d'first Sunday last month' +"%d-%b"