In this sentence 'far' means 'more' or 'much more', so it is used to here to emphasise the word 'greater' even more. One would not use the word 'quite' in this sentence. In other words, it would be incorrect to say: quite greater pain. The correct way to express this would be to say, for example: we remember with a certain amount of pain/a fair amount of pain/some pain/quite a lot of pain, depending on the exact meaning you wish to express.