When is it good to build characters [mascots] into your brand?
– The State Diner, Ithaca, NY
A good logo or mascot can convey instantly what would otherwise take tens or hundreds of words to describe. In your case, Eddy Freshness, the grilled cheese guy, definitely says something. The question for you is whether that message is clear and represents a revenue opportunity. Put simply, if the answer is yes to both, it’s fine and if the answer is no to either, then it’s time to retire Mr. Freshness.
To illustrate, your mascot in particular says, to me, “We are a fun family-friendly restaurant that offers a variety of delicious options. Allow me to draw your attention in particular to our grilled cheese, which is one of our signature items. Children will be especially pleased by this menu offering.”
The first question for you is whether that is an accurate interpretation. Some basic market research in informal interviews or a formal focus group can give you an indication of whether other guests share this interpretation.
The next question is whether sending this message will have the desired effect. Is grilled cheese a particularly important section of the menu that you want to emphasize in the menu mix? Can it become a star (a high margin, high demand item)? Given its relatively low food cost, opportunities to upsell by adding bacon, tomato, premium cheese and so on, and its ease of preparation, I would guess that the answer is yes.
Following that process can help you evaluate your overall communication piece-by-piece, whether it's a logo, a mascot, a photo, or a menu description.
More on marketing with mascots here.