Why is she saying “bang him on the counter” when he is a small living thing?

verb /baNG/ 

Strike or put down (something) forcefully and noisily, typically in anger or in order to attract attention

• he began to bang the table with his fist
• Sarah banged the phone down
• someone was banging on the door

However in Britain it just means to put something down (casually as Malvolio suggested).
Typical expression: Just bang it in the corner there

I would like to think, that the author is referring to the Dead parrot sketch from Monty Python

PS: Bung has the same meaning in British slang: Bung it on the table

To an American, "bang" can only mean to put something somewhere with destructive force. To a Brit, however, "bang" can make to put something somewhere casually, without much effort or attention. I once heard a Englishwoman say she intended to "bang up some wallpaper" (an American would have said "throw" in the same context).