Oh dear!
I think I smell a rat .. well, not actually smell one, but there are signs.
After suffering damage to several bananas, but never to ones that were sealed in bags, we sprinkled some flour round the banana stand (where the bananas stand) on the kitchen table. And sure enough, this morning when we got up, the flour was disturbed, and there was a trail of foot prints across the table.
The strange thing is, we've had mice before, and you can hear them rampaging and crashing around the place. This creature is as quiet as a err .. not mouse.
Hey ho! A 'phone call to the Rat Catcher, methinks.