even is not idiomatic. It adds a new information.
Without even, we only know that her dog doesn't want to eat her cooking. We have no information if she has tried to offer her cooking to other animals or persons.
With even, we know/assume that there have been several/many attempts to offer her cooking but nobody wanted to eat it. Each offeree was picky to some (different) extent. But no-one wanted to eat it. Neither the least picky one (her dog).
This would be a neutral understandig of facts in the second sentence. But the second sentence can also be used as an offense. In truth, there have been no attempts to offer her cooking to anyone (besides the speaker perhaps). Nevertheless, the speaker wants to present her cooking as unfavourably as possible and pretends/implies that such attempts have taken place with the result that no-one accepted her cooking. Neither her dog.