@JS
When you say “they claim to take it off the total” is the amount listed or just shows the lump sum of the car and therefore have to take their word for it.
My situation maybe different from usual because when I lost higher rate in the change to PIP temporally, I bought my car but no GCB was showing on the offer price but having a look back at the letter Motability sent me they said my DLA payments from the DWP would stop on the 21st November and my 3 year term finished on the 27th November.
Either the GCB does not show on the offer price or I was done out of a GCB simply because of the 6 days between the two dates noted above.
Water under the bridge now but going by what Dave h said, you get a cheque in the post and not deducted from the offer price so looks like I was robbed.