I guess I shouldn't be. Even letting them know you were fully aware you were breaking the law, most people would see its intended purpose -- to bring a little peace and comfort to a very old woman -- and have their own compassion kick in.
YMMV but I'm guessing you'd hear something along the lines of "Oh,... well,... (shuffles feet) ... just turn it off, then". Many of us have elderly people in our lives we wish we could provide some comfort to and most of us know we're headed there (if we're lucky to live that long). You know, assuming your 20m radius FM transmitter didn't, say, cause some cataclysmic event/knock emergency services offline for several city blocks, etc.
Put another way, while some police actually will pull you over and write you a ticket for going a couple of miles (km) per hour over the speed limit, most won't waste the brain power/physical energy/thermal paper to bother enforcing it.