It's not so much the
pieces of plastic I'd be worried about but, what is actually contained in the plastic. So yeah, I'd be concerned with them eating it
.
Was it a large amount of meat? Perhaps save the chunky ground and see if you can feel any plastic in it and throw the fine ground out?
By any chance, did you keep the packaging from the meat? Or the receipt? I'd look for the manufacturer's phone number and address. Call and let them know what happened and that you have meat wasted. Follow up with a letter and a copy of the receipt. It would be good customer service if they refunded you the amount of $$ lost.
Btw, if you have a restaurant supply store near you, you can get a really good quality "pusher" that you won't have to worry about breaking or chipping.