Thanks so much. I'll have another look, but it appeared to be attached only at the end of each "arm", and yes, I do have the plate off. That's a great suggestion to restore the bolts.
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It turns out, once I had enough light to peer into the grille, that the license plate bracket is attached to the car with 10 mm bolts passing through holes at the end of the plastic arms of the bracket and into self tapping metal brackets. It also turns out that the left bracket bolt also secures the (feeble) horn, so removing the bracket - once you've laboriously tried various sockets - no Philips heads here - to identify which might work - is not so much a task as is reinstalling it to also retain the horn. This requires shimming, and thus much experimentation with washers, all of which fall into the front grill area because you barely can get your hands in there. I finally resorted to a nut as a shim, after four times losing the washers I'd piled onto the bolt. It's one of those simple, five minute jobs that can take an hour, make your back hurt, and leave deep welts on your wrists. Otherwise, no problem. It sure does look better without the billboard on the front of the car. By the way, I've just bought it, my dream car, basically.