Bukhari

Hadith Commentary:
Or it refers to your wife.
By all of these, what is meant is women who are not mahram.
Even in the pledge of allegiance (bay‘ah), you did not touch their hands.
In the narration of al-Nasa’i and al-Tabarani, it is stated as follows:
Umaymah bint Ruqayqah came to the Messenger of Allah (sallallahu alayhi wa sallam) along with several women and requested to shake hands.
He (sallallahu alayhi wa sallam) said: I do not shake hands with women.

Hadith Commentary:
(1)
The true state of hearts is known only to Allah; however, it was deemed necessary to conduct an outward examination of the women who migrated, to ascertain whether they were truly Muslim and had left their homes solely for the sake of Islam, and not due to any worldly or personal motive. Was it not the case that they had migrated out of anger towards their husbands, or due to domestic issues and household disputes, or merely for travel and sightseeing, or for some other purpose unrelated to Islam?
(2)
Since the addressees of this command are the believing men, not the Messenger of Allah (sallallahu alayhi wa sallam), the Messenger of Allah (sallallahu alayhi wa sallam) selected Sayyiduna Umar (radi Allahu anhu) for this purpose, and he would examine the women who arrived in Madinah Tayyibah.
After this examination, those emigrant women—and indeed, all Muslim women—were commanded to pledge allegiance (bay‘ah), and this pledge was taken by the Messenger of Allah (sallallahu alayhi wa sallam) himself, because the verse regarding bay‘ah addresses him directly. The sins from which the pledge was taken to abstain were all major sins (kabirah), and at that time, these were commonly practiced in Arabia. The details of this pledge are mentioned in Surah al-Mumtahanah, verse 12 ().
And Allah knows best.

Hadith Commentary: Benefits and Issues: After the Treaty of Hudaybiyyah, when the way was opened for Muslim women to migrate from Makkah to Madinah, because they were not included in the agreement of return, or Allah, the Exalted, commanded that they be exempted, and the disbelievers also did not object to this, then Allah, the Exalted, commanded His Messenger sallallahu alayhi wa sallam to examine their faith: whether they had truly migrated solely for the sake of Allah and His Messenger, or whether the background was hatred for their husbands, love for someone else, or worldly greed. If they were firm and steadfast in faith, and the migration was solely for Allah and His Messenger, then he would accept their pledge (bay‘ah), and the conditions of the pledge were also stated. Any woman who acknowledged these conditions would be considered successful in the test, and he would take the pledge from her verbally, without taking her hand in his, and would order her to go. If the Messenger of Allah sallallahu alayhi wa sallam did not shake hands with non-mahram women, then how can the followers be permitted to do so?

Benefits and Issues:

➊
The complete words of the verse mentioned in the hadith are as follows:
﴿يَا أَيُّهَا النَّبِيُّ إِذَا جَاءَكَ الْمُؤْمِنَاتُ يُبَايِعْنَكَ عَلَىٰ أَن لَّا يُشْرِكْنَ بِاللَّهِ شَيْئًا وَلَا يَسْرِقْنَ وَلَا يَزْنِينَ وَلَا يَقْتُلْنَ أَوْلَادَهُنَّ وَلَا يَأْتِينَ بِبُهْتَانٍ يَفْتَرِينَهُ بَيْنَ أَيْدِيهِنَّ وَأَرْجُلِهِنَّ وَلَا يَعْصِينَكَ فِي مَعْرُوفٍ ۙ فَبَايِعْهُنَّ وَاسْتَغْفِرْ لَهُنَّ اللَّهَ ۖ إِنَّ اللَّهَ غَفُورٌ رَّحِيمٌ ﴾
“O Prophet (sallallahu alayhi wa sallam)! When believing women come to you to pledge allegiance to you that they will not associate anything with Allah, nor will they steal, nor will they commit adultery, nor will they kill their children, nor will they bring any slander which they have invented between their hands and feet, nor will they disobey you in what is right, then accept their pledge and ask Allah to forgive them. Indeed, Allah is Most Forgiving, Most Merciful.”

➌
You would also take this pledge from women that they would not engage in wailing and the like.
In the narration of Sunan Abu Dawud, a female companion (radi Allahu anha) said:
Among the good deeds regarding which we were made to promise that we would not disobey the Prophet (sallallahu alayhi wa sallam) was also included that we would not scratch our faces (causing injury), nor wail (nor lament), nor tear our collars, nor dishevel our hair. (Sunan Abu Dawud, Book of Funerals, Chapter on Wailing, Hadith: 313)