Giving Salaam on entering the masjid.

Bismillahir Rohmanir Roheem

To greet a Muslim brother or sister with Asalaamu Alaikum is a blessing. In the Sunnah of Rasulullah ﷺ, innumerable virtues are mentioned. Although there are certain times, not to give salaam to the Muslim brothers or sisters. 

The Fuqeha have also listed certain moments when someone salutes, they must not give an answer, so that he/she becomes aware that this is not a moment or place to salute.

One of the moments and places is when you enter the mosque. One should not greet each other in the mosque, especially when it comes to someone waiting for the prayer.

People who wait for prayer are themselves in ibadah (worship), even though they are not engaged in tasbeeh or any other kind of zikr. Waiting for prayer is itself a worship. So in such a moment, it is not allowed to give the salaam or musafaha (handshaking). One should quietly go into the mosque and keep himself busy in the zikr of Allah.

The fuqeha themselves have mentioned this that if someone comes and does Salaam (knowingly or ignorant), one should not give an answer. The reason is so that one is then informed that this is not a moment or place to give the salaam.

And Allah knows best.

السلام تحية الزائرين، والذين جلسوا في المسجد للقراءة والتسبيح أو لانتظار الصلاة ما جلسوا فيه لدخول الزائرين عليهم فليس هذا أوان السلام فلا يسلم عليهم، ولهذا قالوا: لو سلم عليهم الداخل وسعهم أن لا يجيبوه، كذا في القنية.    (الفتاوى الهندية 5\325)

يكره السلام عند قراءة القرآن جهرا، وكذا عند مذاكرة العلم، وعند الأذان والإقامة، والصحيح أنه لا يرد في هذه المواضع أيضا، كذا في الغياثية. (الفتاوى الهندية 5\325)