The amount of what given to the customer? Cash? - None Grief? - Could be a little or a lot. Satisfaction? - could be a lot, could be a little, could be none.
When a customer complains, usually to the dealer’s service writer, the dealer addresses the complaint in terms of warranty work done to the car and charged back to the manufacturer. Note: dealers are independent franchises, not owned by the manufacturer.
If the repair doesn’t meet the customer’s satisfaction, they can elevate the complaint to the zone representative of the manufacturer. That might get another attempt at repair or the engineers may be engaged to assist the dealership but little else.
In the event of a car defined under the owner’s state “lemon” laws, the manufacturer will be required to buy back the car. State laws vary. In a rare instance, the manufacturer may get sued in civil court.
I was formerly an engineer for a major automaker. My first car purchased at discount from that automaker was, by far, the worst car I have ever owned and that includes 2 used cars purchased with over 90,000 miles. 14 trips to the dealer for 27 separate complaints. Two that were repaired unsuccessfully at least 5 times. Long before lemon laws. So, been there done that.
My last new car has never been in for a warranty complaint and it is now 14 years old. Oddly enough, from the same manufacturer as the worst.