Bukhari

Hadith Commentary:
The prohibition against eating the meat of domestic donkeys is for the purpose of making it unlawful (tahrim), whereas the prohibition regarding eating garlic is for the purpose of discouragement (tanzih). However, there is no harm in eating it after it has been cooked.
One should not come to congregational prayer or gatherings of people after eating raw garlic.
Since angels would come and go in the presence of the Messenger of Allah (sallallahu alayhi wa sallam) at all times, he never consumed garlic.
And Allah knows best.

Hadith Commentary:
(1)
According to the opinion of some scholars, the Messenger of Allah (sallallahu alayhi wa sallam) issued the aforementioned prohibition regarding eating garlic either when going to or returning from the Battle of Khaybar. They understood from the hadith that "mosque" refers to the Prophet’s Mosque (Masjid Nabawi). However, a hadith narrated from Abu Sa’id (radi Allahu anhu) in Sahih Muslim shows that the Messenger of Allah (sallallahu alayhi wa sallam) issued this directive after the conquest of Khaybar. On this basis, "mosque" does not refer specifically to the Prophet’s Mosque, but rather to the place in Khaybar that was prepared for performing prayer, or it refers to the general category, meaning that such a person should not come to any of the Muslims’ mosques. Accordingly, in Musannaf ‘Abd al-Razzaq it is mentioned that Ibn Jurayj asked his teacher ‘Ata’ whether the aforementioned prohibition of the Messenger of Allah (sallallahu alayhi wa sallam) was specific to Masjid al-Haram or included all mosques. He replied that this ruling applies to all mosques.
(al-Musannaf li ‘Abd al-Razzaq: 1/444, 445) (2)
It is strictly prohibited to bring any foul-smelling thing into the mosque or to come to the mosque after eating it, because it causes harm to the people. Besides this, the mosque is in any case a pure place where Allah is remembered, so under no circumstances should its sanctity be violated. Raw garlic, onions, radishes, cigarettes, and bidis all have the same ruling. The only difference is that garlic, onions, and radishes can be used after cooking, because doing so removes their odor, but smoking tobacco and bidis is not permissible under any circumstances. The scholars of the Arab lands have issued a fatwa declaring it forbidden.

Benefit:
It is prohibited for a Muslim man to stay behind from the congregational prayer without a valid excuse. The meaning of this hadith is not that eating something with a bad odor is a reasonable excuse to stay behind from the congregation; rather, the intended meaning is that when the time for prayer is near, one should avoid using such things.
Similarly, women should also be careful when praying at home, ensuring that they do not consume raw garlic or onions before the prayer.