"Okay, so you heard me type in the PIN? So now you can know my PIN?"
"Oh no", he said, "it's just beeps, like this - ", and pressed a few digits.
"Right so you typed 1 6 3 2 4, there."
"..."
"That's what you typed, isn't it?"
"Uhm... yes, how did you guess?"
"I didn't guess, I could hear the beeps. I've got a reasonable ear for pitch, so I can tell what the numbers are from the tones. Any chance you could escalate this to your manager after the call, and tell them to give me a phone if they've any questions?"
They rang me the next day, and I explained the situation to them.
Now, at least in the UK, you get transferred away from the call handler when you put your PIN in.