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 this Christmas.
See also: on, score, that

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.
See also: on, score, this

on that (or this) score

so far as that (or this) is concerned.
See also: on, score, that

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.
See also: on, score, that, this