Hmmm - I'm not Jody - BUT the part where you aren't supposed to put that into your bank account - is because that is traceable - and if there is a problem with the check, etc. - then that could be tracked.
It might be legit - but honestly - it sounds like a money laundering scheme to me - much more so than anything having to do with being a mystery shopper (except so far as spending the $$$ part!!!) Honestly - what would I do? I would probably be on the phone to the cops and ask them.