I heard some scholars saying that the matter of making remembrance of Allah is left unrestricted. Can you please provide me with proofs from quran, sunnah, ijma’ and qiyas?

It is established in shari'ah (Islamic law) that the matter of making Dhikr is unrestricted. If Allah Almighty legislated that a matter to be open and it entails more than one aspect in doing it, it must be applied unrestrictedly.

Although the matter of making remembrance of Allah [Ar.dhikr]—whether audibly or silently after the prescribed prayers—is unrestricted, it is also a debatable issue. Allah has made the matter of remembering Him, after the prayers, open and unrestricted. He Almighty says:

When you have performed the prayers, remember Allah, standing, sitting down, or lying on your side [4:103).

Therefore, the matter must be applied unrestrictedly unless there appears in the Shari'ah a law limiting it.

The Divine injunctions in the Qur`an on making dhikr is general. This includes:

O ye who believe! Remember Allah, with much remembrance; and glorify Him morning and evening. [Qur`an 33: 41-42).

And keep yourself content with those who call on their Lord morning and evening, seeking His face. [Qur`an 18: 28).

When ye have performed the prayers, remember Allah, standing, sitting down, or lying down on your sides. [Qur`an 4: 103).

In the Qudsi hadith:

Abu Huraira (may Allah be pleased with him) narrated that the Messenger of Allah (peace and blessings be upon him) said: " Allah says: I am as my servant expects Me to be, and I am with him when he remembers me. If he thinks of Me, I think of him. If he mentions Me in company, I mention him in an even better company. When he comes closer to Me by a hand’s span, I come closer to him an arm's length. If he draws closer to Me by an arm's length, I draw closer by a distance of two outstretched arms nearer to him. If my servant comes to Me walking, I go to him running." [Bukhari and Muslim).

A general injunction must be implemented as such until something comes to restrict it.