An EIN is an Employer Identification Number and in the greater scheme of things it is irrelevant nonsense for an MSC to require it UNLESS they are also allowing you to subcontract work--which they do not do.
There is no cost to getting an EIN and it is easily obtained on line. It does not complicate the Schedule C reporting of your mystery shopping business. BUT . . .
In my jurisdiction an EIN is flagged by local government as a business that needs a business license, to meet all required business inspections etc. etc. This also means that in areas which are zoned 'residential only' there may be some issues. In other areas, none of this is an issue. Check with your local government.
My personal choice was to ditch any MSC that insisted on an EIN.