However the insurance is there to cover you, it is quite possible they cannot be bothered to do the claim and so are possibly being untruthful.
I would send another form or whatever is the procedure for the insurance you have taken out.
But did you mean the plate was 81 cents or dollars ?
If it was 81 cents and they paid by PayPal then I would just do a partial refund, not not a new payment.
Don't rush because of buyer laziness, what proof have they of the breakage, could just be after a discount, check their previous feedback to get an idea