There are several things a third-party can legitimately do to repair a laptop display problem:
1) Check if it works on an external monitor
2) Run manufacturers test/diagnosis software on it
3) Check/replace the cable
4) Check/replace the backlight/inverter
5) Check/replace the screen
6) Apply a software/operating system fix
It makes no sense to say, "repair the graphics chip on the board." You wouldn't repair something unless it's damaged. A damaged graphics chip is unrepairable.
I would go back and ask them to break down the costs into labour charge and cost of parts. £70 for a new screen, fitted, is a really, really good price. If it's £70 for labour only, chances are he isn't even going to take a screwdriver to it. It'll likely be a software fix.