on that/this score
on that score
Regarding a certain person, situation, outcome, or possibility. The police have done a lot to make the city safer—on that score, it's been a really positive past few years. I already got the kids' presents, so we don't need to worry on that score.
on this score
Regarding this particular person, situation, outcome, or possibility. Politicians have been actively engaged in discussions around affordable housing, and we've made a lot of progress on this score in recent months. It's on this score that we need to focus the attention of our next board meeting.