The logic will generally look something like this, just to make sure that you've got it down right:
1) Player completes level X and sets a score, let's call it a global variable LevelScore.
2) Compare score to currently saved high score (compare as a number), called WSLevelXScore or whatever.
3) If the current score is higher, set WSLevelXScore to LevelScore.
4) Then you set your text objects on the level select screen.
The last bit is tricky, because it requires that you set each text object individually. You could create ten different text objects, but its much easier to create one and clone it nine times. Each time you clone it, you're adding 1 to its IID (instance ID, starting from 0). So to set the scores to each of them, do something like this:
System : On Start of Layout, Repeat 10 times, Pick nth instance (ScoreText)(loopindex) -> Set ScoreText Text to WebStorage.LocalValue("WSLevel"&loopindex+1&"LevelScore").
I've attached a quick example of the last bit.