My calling card and my parents' calling card. Connect together. Will the message that I deleted the chat record be seen?

You can actually rest assured of this, although your phone card is connected with your parents' phone card. It is very likely that you have a family number, and then you call the other party, and you are probably not needed. If you pay a penny, your parents can pay the money between you, but your parents can't see your chat record, and it is impossible to see it. Even if you are the one who wants to chat with you now, if you two send each other WeChat, your parents won't know.