Question:
Is it permissible to make Hymen restoration surgery ?

Answer:
It is necessarily known in religion that Islam encourages chastity, regards fornication as an enormous sin, and commands barring anything leading to it, such as glances and private meetings [between males and females]. Allah the Almighty says: And do not approach fornication: it is an outrage and an evil path, [17:32]. Indeed, Islam calls for the administration of a punishment for fornication if it reaches the authorities. Allah says: Flog the fornicateress and fornicator one hundred times, [24:2].

However, the basic principle in the Shari‘ah is to cover up [sins] to protect reputations, as is stated in the hadith related by ‘Abd Allah bin ‘Omar (may Allah be pleased with them both) that the Messenger of Allah said:
Muslims are brothers to one another. A Muslim does not oppress a fellow Muslim, nor does he hand him over to an oppressor. Allah fulfills the needs of whoever fulfills the needs of a fellow Muslim. Whoever relieves a burden from a fellow Muslim, Allah will relieve him of one of the discomforts of the Day of Judgment. And whoever covers [a fault] for a Muslim, Allah will cover for him on the Day of Judgment.
We have also been forbidden from spreading [fornication] by publicizing it and by divulging our sins which Allah has covered up. Allah says:
A painful punishment waits in this world and the next for those who like indecency to spread among the believers: Allah knows and you do not, [24:19].
It has been related through Abu Hurayrah, who heard the Messenger of Allah say: All members of my community are pardoned except those who announce their sins.

Among those who announce sins is someone who commits a sin at night; Allah has concealed it, yet when morning comes he says: “O, so-and-so! Yesterday I did such-and-such.” He spent the night with his sins covered by his Lord, and when he wakes, he exposes what Allah has covered.1

The Hanafis have stated explicitly that a virgin who loses her virginity by fornicating in secret (which means that it has not been made known to the court and resulted in punishment) or does not do it repeatedly so it becomes a habit, is legally a virgin even though she is not truly a virgin. She is married as a virgin; she is even not asked to verbally consent to marriage since she is given the same status as that of a virgin, whom the Prophet says said: “Consent is sought from Virgins. Their consent is in remaining silent.”
The Hanafis state that the rational cause here is that asking for her verbal consent would expose her shameful deed, while the Shari‘ah recommends concealment.2 In the same chapter and section, Nasb al-Rayah includes:

Abu Hanifah, may Allah grant him mercy, holds that if people know her as a virgin, they will chastise her if she consents verbally. Thus, she refrains; silence suffices so she is not cut off from her interests.3

Based on the above, it is permissible to medically reconstruct this membrane in order to prevent scandal which would otherwise occur. It is also permissible for a physician to perform such a surgery, even for payment. If the woman is known for promiscuity or has been punished for such acts, then it is not permissible to undergo such an operation due to the absence of the rational cause.
The answer to the question is known from the above.
And Allah the Almighty knows best.
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1. Sahih al-Bukhari, it in the chapter on manners.
2. Al-Anhar fi Sharh Mutlaq al-Abhar, in the chapter of marriage, in the section on guardians and suitable matches.
3. Nasb al-Rayah, in the chapter of marriage, in the section on guardians and suitable matches.