Answer:
Attractive or appealing.
Step-by-step explanation:
Based on the sentence frame and meaning, the word "winsome" is suggestive of an appearance or expression that is hard to resist or deny. The speaker also mentions that it was a "look which turns off bad temper even when one has all the right in the world to indulge it." So, for the new word to have the same effect or meaning, it can be replaced with the words "attractive" or "appealing", which have the same meaning. They also have the same implication of the irresistible and pleading expression that the sentence demands.