Pins 0 and 1 are also used for communication with a PC. So (part of) what you're seeing is what you send to the GSM and what you receive back.
Further there should never be a reason to use SoftwareSerial on the hardware serial pins.
From, the below snip of the pcb, you can choose between SoftwareSerial on pins 2 and 3 or HardwareSerial on pins 0 and 1.
And the relevant part of the schematic
Images copied from https://cdn.sos.sk/productdata/b1/b9/494f8af8/arduino-mc60e-gsm-gps-ble-shield.pdf