Write to serial port by detecting a RFID card

 else
  {
    Serial.write(6);
  }

This is causing the squares. Why the program should print it I do not know.

Try this example from the Instructables page

#include <RFID.h>

/*
* Read a card using a mfrc522 reader on your SPI interface
* Pin layout should be as follows (on Arduino Uno):
* MOSI: Pin 11 / ICSP-4
* MISO: Pin 12 / ICSP-1
* SCK: Pin 13 / ISCP-3
* SS/SDA: Pin 10
* RST: Pin 9
*/

#include <SPI.h>
#include <RFID.h>

#define SS_PIN 10
#define RST_PIN 9

RFID rfid(SS_PIN, RST_PIN);


int led = 7;
int power = 8;
int serNum[5];
int cards[][5] =
{
  {5, 117, 21, 219, 190}

};

bool access = false;

void setup()
{
  Serial.begin(115200);
  SPI.begin();
  rfid.init();
  pinMode(led, OUTPUT);
  digitalWrite(led, LOW);
}

void loop()
{
  if (rfid.isCard())
  {
    if (rfid.readCardSerial())
    {
      Serial.print(rfid.serNum[0]);
      Serial.print(" ");
      Serial.print(rfid.serNum[1]);
      Serial.print(" ");
      Serial.print(rfid.serNum[2]);
      Serial.print(" ");
      Serial.print(rfid.serNum[3]);
      Serial.print(" ");
      Serial.print(rfid.serNum[4]);
      Serial.println("");
      for (int x = 0; x < sizeof(cards); x++)
      {
        for (int i = 0; i < sizeof(rfid.serNum); i++ )
        {
          if (rfid.serNum[i] != cards[x][i])
          {
            access = false;
            break;
          }
          else
          {
            access = true;
          }
        }
        if (access) break;
      }
    }
    if (access)
    {
      Serial.println("Welcome!");
      digitalWrite(led, HIGH);
      delay(1000);
      digitalWrite(led, LOW);
      digitalWrite(power, HIGH);
      delay(1000);
      digitalWrite(power, LOW);
    }
    else
    {
      Serial.println("Not allowed!");
      digitalWrite(led, HIGH);
      delay(500);
      digitalWrite(led, LOW);
      delay(500);
      digitalWrite(led, HIGH);
      delay(500);
      digitalWrite(led, LOW);
    }
  }
  rfid.halt();
}