How can one confess to one's father or mother what happened by way of zina, without tearing the hymen, in order to get rid of the sin?

You must initiate repentance to Allah, the Almighty and All-Glorious, for fornication, by ceasing the sin, regretting it, and resolving never to return to it. It is not a condition for the validity of repentance that you marry the girl; rather, you must sever all ties with her.

If both of you repent with a sincere repentance and you are able to marry her, then there is no impediment. If you are unable, then there is nothing upon you.

It is impermissible to inform anyone of this heinous act; rather, you must conceal yourself and her, based on the Prophet's (peace be upon him) saying: "O people, it is time for you to desist from transgressing the limits of Allah. Whoever commits any of these abominations should conceal it with the concealment of Allah, for whoever exposes himself to us, we will impose upon him the Book of Allah."