It is illegal to fumigate a home if you do not have a target pest.
The infestation must be ID. By a licensed pest control inspector... The EPA label and state laws requires a target pest... termites. Wood boring beetles.
The lender has no say in this matter nor the buyer or any one else. Only a licensed pest inspector can make the ID and the call for the application of a pesticide or for Fumigation ( Tenting the home )
Hope this helps
Excellence Exterminating Co. Inc.