I don’t think any of that is necessary Kezo. They’ve collected the car, the PIN was input at the time, end of story. Even if the £420 really was owed, the dealership has been negligent or at best forgetful in not charging them at the time. However if what the OP says is accurate, then the digital dash became a standard feature before the build date and the £420 should have been refunded or deducted from the AP on collection day. I would advise the OP not to pay.
I agree with what you say r would I pay, however save the dealer ringing and nagging I’d email saying I’m seeking advice. That I expect would be the end of it, because (a) it ain’t worth them pursuing for such a small amount (b) there not likely to win.