If the extract is not too far in the past it's pretty easy:
1) run datapump on live with the following config
expdp user/pass tables=schema.table flashback_time=to_timestamp(some time here, followed by the timestamp format) dumpfile=test.dmp
If that works without error then you have your old copy of the table in the file test.dmp
2) Copy this file to the test db and
impdp user/pass table_exists_action=TRUNCATE
This will truncate the test table and insert all the 'old' live data into the table.
You can use the backup you have - but you can't extract directly from it.
You'll need to restore that backup to some other database name ( as i assume you dont want to overwrite the running system...) - once that database is at the correct point in time you can then use export/import as normal to extract the table that you want.