1؎: If there is a group of women, then there is no harm in greeting them with salam. However, if a woman is alone and the one offering salam is not her mahram, then (in the absence of any fear of temptation) it is better not to offer salam, so that one remains safe from temptation and the like.
Explanation & Benefits
Shaykh Umar Farooq Saeedi
Benefits and Issues: It is Sunnah to greet (say salam to) non-mahram women in situations where there is fear of temptation (fitnah) or suspicion (shubhah). Especially for the elders and seniors of the community, this is a recommended (mustahabb) act.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 5204
´Asma bint Yazid said:` "The Messenger of Allah(ﷺ) passed by us, among (a group of) women, and he greeted us with (the greeting of) peace."
Maulana Ataullah Sajid
Benefits and Issues:
➊ If there is no fear of temptation (fitnah), a man may greet (say salam to) a non-mahram woman, and a woman may greet a non-mahram man.
➋ The situation in which there is no fear of temptation is, for example: If the woman is elderly, or there are several women present, and there is no risk of any misunderstanding arising, then a man may greet them.
➌ For a young woman to greet a man alone, or for a man to greet a young woman, can lead to problems; therefore, it is necessary to avoid this. However, a mahram man and woman may greet each other, and in fact, they should greet each other, because in this case there is no danger of inappropriate thoughts arising.
Source: Commentary on Sunan Ibn Mājah by Mawlānā ‘Atā’ullāh Sājid, Page: 3701