The act of kissing the thumbs when the name ‘Muhammad’, may Allah’s choicest peace and blessings be upon him, is mentioned is a practice of reverence and love for the Beloved Messenger of Allah.
It was first established by the master of Companions, afzaal ul bashar baad al-Ambiya (superior over all mankind after the Prophets), Sayyidina Abu Bakr Siddique – read here about his utmost love for the Beloved Messenger of Allah.
It is narrated by Imam Daylami in his Musnadul-Firdaws:
Whenever Sayyidina Abu Bakr Siddique heard the mu’azzin say, “I bear witness that Muhammad is the Messenger of Allah”, he would repeat this phrase and would kiss the tip of the index fingers (or thumbs) and wipe his eyes. The Prophet said, “Whosoever does what my friend (Sayyidina Abu Bakr) did, my intercession will be upon him.”
A similar narration is reported by Imam Isma’il Haqqi in his Tafseer Roohul Bayaan. In that narration, Sayyidina Abu Bakr Siddique is asked by the Beloved Messenger why he kissed his thumbs in such a manner. He replied, “Qurratu ayni bika, Ya RasulAllah!” or “You are the coolness of my eyes, O Messenger of Allah!”
Regarding this incident as reported above by Imam Daylami, Mulla Ali Qari states, “If it can only be established as a saying of the Siddiq (Sayyidina Abu Bakr), it would be enough as a basis for practice, because of the Prophet’s saying:
‘You must follow my Sunnah and the Sunnah of my Rightly-Guided Successors.’” [al-Asrar al-Marfua fil-Akhbar al-Mawdua] Another version of this Hadith states, “My Sunnah and the Sunnah of my rightly guided Caliphs is obligatory upon you.” [Abu Dawud, Hadith no. 4607; Tirmidhi, Hadith no. 2676]
Imam ibn Abidin states that thumb-kissing is desirable (mustahabb) when hearing the azaan, together with invoking blessings on the Prophet and adding, “Welcome, my beloved and the coolness of my eyes!” then asking for healthy sight and hearing. [Hashiya 1:398]
The great Mujaddid of our times, Imam Ahmad Raza Khan, has compiled a text of two-hundred pages entitled Munir al-Ayn fi Hukmi Taqbil al-Ibhamayn, meaning ‘enlightening the eyes by kissing the thumbs.’ In it, he clarifies the permissibility of this act and refutes objections raised against it.
To conclude this topic, remember that the Companions of the Beloved Messenger of Allah, may Allah’s choicest peace and blessings be upon him, often expressed their love and devotion towards him in different ways, through different acts. They didn’t ask for verification or proof of validity because such love itself serves that purpose.
May Allah’s eternal peace and blessings of the highest degree be upon our Master Muhammad, upon his Family and his Companions.