Configuring PostgreSQL for parallel deletion involves several steps. However, it's important to note that as of my last training data, PostgreSQL does not directly support parallel execution for DELETE operations. Parallelism in PostgreSQL is typically used for queries (e.g., SELECT), but not for data modification commands like DELETE.

That said, you can implement a form of parallel deletion by manually dividing the task across multiple connections or scripts. Here's a conceptual approach using a real-life data set scenario:

1. Data Set Scenario: Suppose you have a large table sales_data with millions of records and a date column sale_date.
2. Indexing: Ensure the table has an index on the column used for deletion criteria (e.g., sale_date), as this makes the deletion process more efficient.
3. Divide the Data: Determine logical divisions of your data. For example, you might divide the sales_data table by date ranges.
4. Parallel Scripts/Connections: Write multiple scripts or open multiple database connections. Each script/connection handles the deletion of a subset of the data. For example, one script could delete rows from 2020, another from 2021, and so on.
5. Batch Deletion: In each script, perform batch deletions to avoid long transactions and reduce load. For instance, delete rows in chunks of 10,000 where sale_date falls within the specified year.
6. Monitor and Adjust: Monitor the database performance. If the deletions are too aggressive and affect normal operations, adjust the batch size or the interval between deletions.
7. Vacuuming: After the deletion, run VACUUM (or VACUUM FULL if you need to reclaim disk space) to clean up the table and update the statistics.

While this approach doesn't use built-in parallelism for deletion, it achieves a similar effect by manually distributing the workload. Remember to test any deletion strategy on a non-production environment first to gauge its impact and tweak as necessary.