It seems half removed is when the relative is a relation through only one of your great grandparents and not both so eg. Your great grandfather's line through a different spouse due to death or divorce and not your great grandmother's.

So in Arabic you can describe your brother as sharing both your parents by saying شقيق, eg. أخ شقيق, and you can describe a half-brother either by attributing that brother to your mother or to your father, أخي لأبي or أخ لأب, or أخي لأمي or أخ لأم. You can see this would require you have additional information about the "half-brother".

Another option is to negate the brother being شقيق. Eg. أخي غير الشقيق.

To convey "great-great-great-grandaunt, half removed" clearly in Arabic you would need to convert it to "the half-sister of my grandfather's grandfather"
أخت جد جدي غير الشقيقة

Then if you want to refer to a distant cousin you would say ابن/بنت أخت جد جدي غير الشقيقة

Other suggestions I've seen like بعيد بنصف جيل don't conform with Arabic usage and would parse as gibberish.

Of course, this all depends on my understanding of the term "half removed" and that's why I lowered the confidence level.

I hope this helps.