If they don't have a Class 41 registration, I believe this is the legal dogma – but if they do, no amount of fair use or parody lets you use their mark on a Cla

If they don't have a Class 41 registration, I believe this is the legal dogma – but if they do, no amount of fair use or parody lets you use their mark on a Class 41 service without authorisation. Fair use / parody is US copyright, not trademark. I tried to check whether Hotdog on a Stick had Class 41 registration, but USPTO's TESS has got to be the worst trademark search system I've ever used. I've seen more distinct error pages than useful results, and can't even find their Class 43 registration.