I too own a Fit and live in the chilly climes of New England. I don't know what kind of rodent it was but this time last year some toothsome little bastard got into the engine compartment and chewed through the delicious battery lines that lead to the battery sensor! They also nibbled the tasty plastic box that housed the battery itself. The dealer wanted to replace the entire damn electrical harness for $2K! My local guy was able to fix it for a fraction of that, luckily.
It's cold out and the furry little bois are looking for somewhere out of the elements and our cars are parked outside and seem like a great option! Then they discover the tasty soy-based plastics and wire insulation and ding! Dinner is served! You don't want this to happen. What was extra annoying was that the car still worked normally. It just had a warning light on and presumably it would've affected my fuel efficiency. So my mechanic removed the remains of the battery housing which, delicious as it may be, was extraneous to the functioning of the car, and sprayed a whole lot of anti-rodent spray like this stuff. I think there are some other options on there for indoors that might also be useful for you but this stuff is basically a peppermint spray and doesn't smell that bad at all. I highly suggest you use some of this stuff before they do damage, if they already haven't. I haven't had a problem since. Good luck.
I use this: https://smile.amazon.com/gp/product/B01HEHE28W/
Something like this. https://www.amazon.com/RODENT-SHERIFF-Pest-Control-Spray/dp/B01HEHE28W