Ranges in the pattern syntax use the sorting rules of your collation.
Use a binary collate clause so the range is ordered by character code.
(I also changed it to LIKE as I find that more obvious than PATINDEX > 0)
SELECT *
FROM mbrnotes
WHERE LINE_TEXT LIKE '%[' + CHAR(127)+ '-' +CHAR(255)+']%' COLLATE Latin1_General_100_BIN2