First thing I'd try is a heat gun to loosen the adhesive immediately under the top portion of the badge to separate it from the riveted base block, if you are looking at refreshing the badge that is. If the goal is to remove it completely from the grill then as Jimmy pointed out, you almost have to use a small dremel cut off wheel.

Years ago, I was successful in removing a badge from a grill without cutting. Took careful leverage but, I might have been lucky not to have a grill that that had significant swagging.