The probing is typically performed with a Delmhorst meter. This meter measures the percentage moisture in the wood. The probe of the meter is inserted through the EIFS to the wood substrate. The probe is small and typically no damage is done to the EIFS as a result of the probing. The probe holes are sealed after the probing.
Some companies have more sophisticated probing devices that are nonevasive.
Ask the company about their equipment. The probes are typically taken around the structure underneath windows, around doors and decks, at roof eaves, etc. The company will generate a report. If the report indicates elevated readings, you should promptly consider options to deal with the problem.