BirdCam Nails a Culprit

For some weeks I have marvelled at sudden feeder emptyings at one particular sunflower seed feeder.  I, of course, blamed squirrels immediately.  But a nagging feeling tugged at me and I pointed my faithful BirdCam at the feeder in question.  The answer was all there in black and....yellow.  Just today half the feeder contents (approximately 10 oz. of sunflower seed) disappeared between 10:45 AM and 4:30 PM.  The only birds that showed up on the resulting images were American Goldfinches.  Several exceptionally gluttonous ones.  Maybe more.  And not a squirrel to be seen.  I am not terribly surprised at this indictment.  Finches are exceptionally prodigious feeders.  But what to do?