Answer: Ted’s probably has an infringement claim based on Trade dress appropriation.
Explanation: Trade dress refers to the general appearance of a product that gives customers an idea where the source of the product is from.
In the US, it is a crime to mislead customers as where the product is from, Wally's using a wiener dog with a white hat is misleading as to the product he's selling.
Ted's can file a trade dress suit against Wally's based on the fact that a wiener dog is used as an advert.