From Namaz of a Mu'min:

Lexically the term Taqbīl-e Ibhāmain is understood to mean the kissing of the thumb. However, by and large this term is understood to mean the kissing of the thumb and then brandishing it over the eyes on hearing the name of the Beloved Prophet of Allah şallAllāhu álayhi wa sallam, during the ad’hān, the iqāmah or any other occasion in affection and reverence to Rasūlullah şallAllāhu álayhi wa sallam.

Taz’īm-e Rasūlullah şallAllāhu álayhi wa sallam

A true Muslim always carries out orders of Allah Almighty. The following verse of the Qur’an commands us to pay due respect to the Beloved Messenger of Allah şallAllāhu álayhi wa sallam.

So you believe in Allah and His Rasūl and honour him.

Sharī’āh disseminates the concept of Taz’īm-e Rasūlullah şallAllāhu álayhi wa sallam

It is stated in Fath Ul-Qadīr Sharh Hidāyah and [Fatāwah] Alamgīrī that:

Those deeds, which are intended for respect or honour, are liked.

For centuries it is a customary to perform the Taqbīl-e Ibhāmain in affection on hearing the name of Sayyiduna Rasūlullah şallAllāhu álayhi wa sallam.

The Munafiqīn of the recent era, dislike Taz’īm-e Rasūlullah şallAllāhu álayhi wa sallam

The exasperated Munafiqīn of the recent era, state that this mustahab deed [of Taqbīl-e Ibhāmain] is a bid’ah [innovation] and preclude thus system of showing affection towards Rasūlullah şallAllāhu álayhi wa sallam. The sole objective behind branding this deed as bid’ah is to prevent us from paying due respect on hearing the name of our Beloved Prophet şallAllāhu álayhi wa sallam.

Taqbīl-e Ibhāmain is mustahab, lawful and commendable.

Sayyidunā Abū Bakr as-Siddīq used to practice Taqbīl-e Ibhāmain

Imām al-Daylamī has written is his book, Musnad al-Firdaus that Amīr Ul-Mu’minīn Sayyidunā Abū Bakr as-Siddīq recited the following dū’ā on hearing: I bear witness that Muhammad is the Prophet of Allāh, in the ad’hān:

I bear witness that Muhammad [şallAllāhu álayhi wa sallam] is the devotee and Prophet of Allah Almighty, I am blissful that my Rabb is Allah Almighty, my religion is Islām and Nabi is Muhammad [şallAllāhu álayhi wa sallam].

And then he touched both thumbs and inner surface of both index fingers on to his lips followed by brandishing them over the eyes.

On this, the Beloved Prophet şallAllāhu álayhi wa sallam said,

Whosoever practices this as my loving [friend] has done, will legitimize my intercession. 

Imām al-Ajal ‘Allāma ‘Alī ibn Sultān Harvī Qārī [d. 1014] famously known as Mullah Alī Qārī has written in his book Mawdū’āt al-Kabīr concerning the kissing of the thumbs:

When a link has been proven up to Sayyidunā Abū Bakr as-Siddīq then it is [more than] enough for one to practice this, since the Beloved Messenger of Allah şallAllāhu álayhi wa sallam has said that it is essential for you to practice my Sunnah and that of my honourable righteous Caliphs.