Glass cooktop stove with scratches on it
The photo looks like the glass is pitted rather than scratched.  They don't look to be very deep but it could have weakened the glass enough for it to crack when you turn the heat on.  The worst thing that will happen when you turn on the heat is the glass will crack.  In that case you will need to replace the glass for sure. Just be careful that when you are cleaning the stove top you don't cut yourself if the pits are sharp.