If your hybrid badge was cleanly removed by someone hoping to reuse or sell it, your car's paint and surrounding body panels may be OK. If so, you can likely replace the stolen badge yourself, without getting the insurance company involved.
Your hybrid is likely new, or at most, a few years old, so you should be able to order a new badge for it from the dealership. There are also badge and car brand specialists who catalog late-model car badges. You can find them through a simple online keyword search. A 2008 Ford Escape hybrid badge lists for about $35 and a pair of Toyota Prius badges will set you back around $37. Ask the parts counter person if special chemicals are needed to prepare the adhesive bond before installation.
You're biggest challenge may be getting the new badge located exactly where the old one was. Adhesive residue and surface grime on the car body may help you see where the old badge was located, so hold off on cleaning up the car until you've thought through how you'll place the new badge. Masking off the area with blue painter's tape can frame the "footprint" of the old badge. This will also help to protect the paint, while giving you a precise target for installing the new badge. If need be, you may be able to take reference photos and measurements from a dealership car.
Test the location of the new badge with a paper template, made by tracing around the badge and cutting out its shape. Use a couple of strips of masking tape to hold the template on your car once you're satisfied with the location. Then, make reference marks with a grease pencil and remove the template. Next, you'll need to carefully clean off any remaining grime and adhesive residue, taking care to retain your reference marks. You can warm the old adhesive residue with a hair dryer to make removal easier. Use a tar remover or other paint-safe product to help clean the area, too. When the paint surface looks clean, go over the location with a bit of rubbing alcohol -- but wait until after you've attached the new badge before breaking out the car wax. Practice positioning the new badge a few times before exposing the adhesive on the back. That way, you'll know just how to hold it when you're ready to apply it for good.
For more information about hybrid cars, follow the links on the next page.