I put 'remember rightly' and was marked wrong. However, because "rightly" is an adverb it describes the act of remembering while "right", as an adjective (though sometimes used), should be kept for nouns. The same could be said of "correct" and "correctly."
Unfortunately - or fortunately - not always. Just try and submit your better alternative via the error reporting. If the course authors still do maintenance and agree with your suggestion it will become an accepted alternative. If they do not agree, you will probably never know why, however.