Did Peter and John know about the Church, the Body of Christ, in Acts 3?

No. Peter and John had no knowledge of the Church, the Body of Christ, in Acts 3. They remained associated with the Judaism Christ dealt with and the Kingdom of Heaven message John the Baptist preached: repent and be baptized.

Les explains that when he says Peter and John did not have any knowledge of the Church, which is the Body of Christ, they are still associated with the Judaism that Christ dealt with and the Kingdom of Heaven message John the Baptist preached: repent and be baptized. This is still Peter and the eleven men in the early part of Acts. In the same context, the mystery or secret had been hid from ages and generations but now is manifest to His saints.

What did Peter and John not know in the early part of Acts?

In the early part of Acts, Peter and John did not have any knowledge of the Church, which is the Body of Christ. They were still associated with the Judaism that Christ dealt with and the Kingdom of Heaven message John the Baptist preached, including repentance and baptism.