Final answer:
Integrated test facilities minimize the chance of contaminating a client's financial records by allowing auditors to test fictitious transactions without altering live data.
Step-by-step explanation:
The testing technique that minimizes the possibility that the auditors will contaminate a client's financial records is B) Integrated test facilities. This method allows auditors to insert fictitious transactions into a client’s system and verify that the system processes the data correctly without affecting the actual financial data. The other options, such as test data, controlled programs, and tagging and tracing transactions, involve different levels of interaction with live data or system processes which could potentially alter the actual financial records if not handled with extreme care.