어서라도

'Even by doing X, if that's what it takes'

-어서라도 names a measure the speaker would rather not take but will: 긁어서라도 없애고 싶은 거야 'they want it gone, even if they have to scrape it off.' Three lines here use 위해서라도, 'if only for the sake of' — 건강 관리를 위해서라도 운동을 하자 'let's exercise, if only for our health.' It always implies effort or reluctance behind the choice.