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.
on ˈthat/ˈthis score
as far as that/this is concerned: The accommodation is excellent so I don’t think we need to worry on that score.