Do you think that as per the verse of our Holy Qur’an 33:33, the off spring of our Prophet (Sallallahu Alaihi wa Sallam) i.e. Ali (Radiya Allahu Anhu), Fatimah (Radiya Allahu Anha), Hassan and Hussein (Radiya Allahu Anhuma) and other Imam of Prophet’s (Sallallahu Alaihi wa Sallam) house hold are pure as the Shia's claim?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Your question is about the following verse, Allah Says (interpretation of meaning): {And stay in your houses, and do not display yourselves like that of the times of ignorance, and perform As-Salât (Iqamât­as­Salât), and give Zakât and obey Allâh and His Messenger. Allâh wishes only to remove Ar­Rijs (evil deeds and sins, etc.) from you, O members of the family (of the Prophet SAW), and to purify you with a thorough purification.}[33:33].

Ibn Kathir said about the interpretation of the above verse: 'This is a text which is revealed exclusively concerning the wives of the Prophet (Sallallahu Alaihi wa Sallam) of the members of the family of the Prophet (Sallallahu Alaihi wa Sallam).  The reason why this verse was revealed is the wives of the Prophet (Sallallahu Alaihi wa Sallam).'

There is only one interpretation about the revelation of the above verse….

Ikrima used to call out in the market, (the verse): 'Allah wishes only to remove evil deeds and sins from you, O members of the family of the Prophet (Sallallahu Alaihi wa Sallam) and to purify you with a thorough purification’ is exclusively revealed about the wives of the Prophet (Sallallahu Alaihi wa Sallam).'

It is reported in Saheeh Muslim from Zaid bin Al Arqam that Ahl al-Bayt (the members of the family of the Prophet (Sallallahu Alaihi wa Sallam)) are: "They are the wives of the household of the Prophet (Sallallahu Alaihi wa Sallam), but the members of the family of the Prophet (Sallallahu Alaihi wa Sallam) are also those who were not allowed to take the Sadaqa after him.  He said, ‘and who are they?  He replied: He said: ‘They are the family of Ali, the family of Aqil, the family of Jafar, and the family of Abbas, …"

Therefore, Ahl ul-Bayt (members of the family of the Prophet (Sallallahu Alaihi wa Sallam)) in the verse, it could either refer to the wives of the Prophet (Sallallahu Alaihi wa Sallam), because it is because of them that the verse was revealed, or to all the members of Ahl ul-Bayt.

Anyway, either the verse was particularly revealed about the wives of the Prophet (Sallallahu Alaihi wa Sallam), or it is general about all the members of the family of the Prophet (Sallallahu Alaihi wa Sallam), Imam Ali, Fatimah, Hassan and Hussein, may Allah be pleased with them all, they are all among those whom Allah wanted to remove the evil deeds and sins from.

Imam Muslim reported that Ayisha (Radiya Allahu Anha) narrated, "The Prophet (Sallallahu Alaihi wa Sallam) went out one morning, …… then Hassan bin Ali came, so let him in, then Hussein came and entered with him, then Fatimah came and he let her in.  Then he said: “Allah wishes only to remove evil deeds and sins from you, o members of the family of the Prophet (Sallallahu Alaihi wa Sallam) and to purify you with a thorough purification".

Allah knows best.