I think that this is a red herring unless they are doing so in a way that may make people think that they are the restaurant instead of an independent delivery agent, although the restaurant do allege that Grubhub is misrepresenting themselves.

But yes, in principle they can get into trouble for using trademarks and logos without authorization (menus are fair game), although I suppose it is fair use to mention the names of the restaurants they can pick up food from. Going after them for that shows that they are not doing anything unlawful by running their intermediary service if this is the only thing the restaurants hope might stick.