The inspector is required to inspect the exterior siding and that looks like fiber cement. Fiber cement manufacturers, namely Hardi-Plank, prohibit the attachment of anything to their product. I would have said as much and something like this:
“The pergola was bolted to the house siding which is contrary to the siding manufacturer’s installation instructions. Long-term deterioration of the siding may occur. A further evaluation and service as deemed necessary by a licensed and competent general contractor is recommended.”
P.S. There is likely no footing for the posts. FYI.