I was having a conversation with one of my friends. And then he started talking about someone I didn't want to talk about. So I said, "Forget him". He replied, "Forgotten".
Huh? Like really what does that even mean? Does it make sense?
This is a very normal reply when someone follows what you said. Take an example:
Now onward, you will not make that mistake ~ Done!
Here, 'Done' means the person followed the instruction.
In your case, you asked your friend to 'forget', and he said 'forgotten' which is equal to 'Okay, done!'
Such replies are in past participle and most of the times it's just 'done'. But, I have heard a few replying with past participle.
Book the tickets ~ Booked!