In my country we are overrun by possums (I guess they are close relatives of opossums), originally introduced for their fur, but now eating everything green in sight.
There are tens of examples, from Achatina fulica to Aedes albopictus. Biologists study this since hundreds of years (and nobody listens).
Just imagine how easy it would be to punish the citizens releasing animals into the wilderness if micro-chipping was mandatory. No need to ban imports, nothing.