Many thanks for the information Phil and welcome to L.O.C.
Brilliant service from MK then, if they will come to you, but it would be less hassle all round if they authorised your local Lexus Dealer to correct and arrange suitable payment.
Your problem is best addressed by others,but you might consider joining Lexusman`s site as he deals almost exclusively with SC`s https://forum.lexusownersclub.com/