I think they should let you take the plate back home. it no harms take the plate back home. Good thing you take the photo before it turns to scrap steel.
Unfortunately this story is not very surprising, it's a mentality issue
"This is mine, not yours. I want to throw it away, but it's still mine and you can't have it"
Like VehicleSpotter said, no harm would come from allowing the plate to be taken, it's simply a question of denying because they can, and it gives a feeling of power.