Personally, I would reach out again and continue expressing your fully justifiable concern until a result you're satisfied with is produced.
I don't believe I have to be honest, but just do your research as extensively as possible on the company and you can see if they are a legit company by visiting the link I've included. It will take you to the search page for the Mystery Shopping Providers Association, the official "head honcho", so to speak, when it comes to receiving training for certain types of shops, acquiring a certification level and number to boost your own image and likelihood of being offered and assigned to shops on other sites as well as the database to check the existence of such companies. A reliable, existing and functioning company within the MSPA, should each have a listing including, but not limited to, the name, logo, address and industry they are classified as, company description, industries served, services provided, website, fax number (not always applicable but will be more often than not), a named contact individual with their phone number (which typically will be the same as the main company contact number, sometimes with an extension listed) and finally an email address with which to contact that individual. Just search them here and you should be able to find all the info you would need to determine their legitimacy.
https://mspa-americas.org/search
Good luck! Hope this helped. MSPA is a fantastic resource for anyone interested in mystery shopping and even helps to improve the knowledge and ability of well-experienced shoppers, including tons of articles that tell you everything you need to know about the industry. A basic membership is totally free with different perks provided at each membership level such as a complimentary training course, discounts on subsequent ones and free webinars.