All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
He does not have to tell his parents or apologize to them for committing this sin; instead, he must repent to Allah Almighty and conceal himself, and not tell his parents or anyone else about his sin. Al-Bukhari and Muslim reported Abu Hurayrah as saying: The Messenger of Allah said, “Every one of my followers will be forgiven except those who expose (openly) their wrongdoings. An example of this is that of a man who commits a sin at night which Allah has covered for him, and in the morning, he would say (to people): “I committed such and such sin last night,' while Allah had kept it a secret. During the night Allah has covered it up but in the morning he tears up the concealment provided by Allah Himself.” He has to supplicate a lot for his parents and be careful to be dutiful to them.
We point out that repentance from sin is obligatory in any case, and if one promises his parents to abandon the sin, he should do it.
Allah knows best.