I think this should work for you. You just need a little more complex condition to filter/remove the data based on the pattern you found.
UPDATE TableName
SET COLUMN = LEFT(COLUMN, CHARINDEX('<', COLUMN)-1) +
RIGHT(COLUMN, LEN(COLUMN)-CHARINDEX('</div>', COLUMN)-6)
WHERE CHARINDEX('</div>', COLUMN) > 0
Here is a sample SQLFiddle with how the code works on the sample text you provided above.
Or, in case SQLFiddle doesn't work, here is the code:
DECLARE @var NVARCHAR(max)
SET @var = 'Any text <div style="display:none">HACKED CODE WITH DIFFERENT URLS</div> and any text.'
SELECT
LEFT(@var, CHARINDEX('<', @var) - 1) +
RIGHT(@var, LEN(@var) - CHARINDEX('</div>', @var) - 6)
Update:
I have updated my answer with a solution to modify only those records which have this pattern.