To make this more clear, there are two ways of understanding the expression.
"high" as a category or scoring classification
"highly" as an adverb modifying "scored"
If the word is an adverb, only "highly" is correct. If the word denotes a particular scoring outcome, e.g. one gets scored as "low", "average", "high", "superior", then only "high"--the name of that category--could be correct.
Essentially, either form could be correct, but each one means a different thing. If the scoring is not by categories in which "high" is one of them, the word should be "highly" to modify "scored." And this is true, also, of American English, though many Americans use poor grammar.
"I know (1) is correct in American English." How do you know this?
– James K Feb 14 '23 at 12:32