The tm mark is not a fake, tm is an unregistered trademark.

It should be the r mark on products without registered trademarks, but it should actually be a circle R. It is the mark of "registered trademark", which means that the trademark has been applied for registration with the National Trademark Office and has been reviewed and approved by the Trademark Office to become a registered trademark. The TM mark on the product indicates direct use of an unregistered trademark that has not been approved and registered by the Trademark Office.