In Theatre Manager, 'shredding' credit cards means removing the middle 8 digits of a credit card number so that what is stored in the database is only the first four and last four digits of the number: 1234-xxxx-xxxx-1234. Cards stored in this manner cannot be accessed for use (because those 8 digits aren't masked - they really no longer exist). Users can still search the database for a credit card using the first four and last four digits for reporting and transaction history.
There are two choices for 'Shredding' Credit Cards. The first method, Shredding Unused Credit Cards, allows a venue to set the number of days a credit card is stored in the usual encrypted format in the database (and is therefore available for use as a payment method for post-dated payments or in the patron's credit card tab), and then after that period, a card is considered "unused" and is shredded of its middle 8 digits.
The second method, setting the database to Schedule C: Shred Immediately, will shred cards and never store them in the database. This is rarely used, as it may prevent some common or desirable business functions (and maintaining Schedule D: Encrypted Credit Card data, the default PABP/PCI Compliant method will not prevent those functions).