"I have found a repair shop, he says he can replace the surface protection layer alone, without replacing the whole screen, which will only cost $30, i'd like to give it a try recentely !!!"
There isn't any "surface protection layer" on MacBook Pros made after 2012.
The display just has a thin sprayed-on anti-glare coating.
You DO NOT WANT ANYBODY fooling with this coating.
It's fragile to start with, and any tampering with it will start "wearing it off"
(This is where the term "StainGate" came from)
Best advice:
Next time, keep the cat away from the screen...