The data you are seeing has already been sent by the previous execution of the sketch before the main MCU was reset. That data resides in a small buffer within the USB interface chip (or even within the USB CDC/ACM / USB UART driver itself, depending on your OS) to which you have no access.
You just have to ignore that data. The simplest way is to put a marker at the start of your program to indicate that whatever is receiving the data should start its receiving from this point on. Something like: