K,
You may want to try this, heat it up good and hot for a cook, then take a decent size chunk of dry ice and rub it around the dinger may also hold it on there but I've found a little circular motion helped sometimes. I've had this trick work on motorcycle tanks with dings where afterwards you couldn't tell it had been dented. I've have also seen it fix some of the hail damage on a jap car. We used a heat gun for the heat. Thicker metal like on older vehicles doesn't work as well but this old bodyshop trick may work on your grill. Dry ice is cheap and maybe worth a try. As already mentioned I'm not sure I'd pound it with a hammer at risk of cracking the finish.
Bradley