Ok, so let's assume you have a DOM element in which you display the score, and start with that.
So, the first time the user will arrive on the game, the score will be "0" (you will probably have something to calculate it and that's not the scope of this answer, let's focus on the load and save parts for now.
I'll write the save function in this way:
function SaveData(score) {
localStorage.setItem('save', btoa(score));
}
While, the load function could be like:
function LoadData() {
var score = window.localStorage.getItem('save');
if (score === null){
score = 0;
}else{
score = atob(score);
}
document.getElementById('demo').innerHTML = score;
}
I've used the btoa an atob, but they are unnecessary to save just a number, but since you used them I suppose there will be a reason, I deleted the JSON.stringyfy (and not added the parse) because that's totally unnecessary and could be trivial, because you will end up with an object (or an error)