Hold on, I'm, going mad. Let me work this out!
So, you're connecting to the Arduino pins D0, D3, D4, D5, D6, D8, D9, D11. That's going to use the serial ports RX on D0 so let's use pins from D2 to D9 for you so I can start afresh.
They have wired a 5 x 3 matrix but they've used 10 pins instead of only 8. The middle column has been split across 10, 7 and 3.
So, first join 10, 7 & 3 together on your keypad and we'll call the combined column 20 (10 + 7 + 3).
Now we have the following layout:-
9 - Â 1 Â Â 2 Â Â 3
8 - Â 4 Â Â 5 Â Â 6
6 - Â 7 Â Â 8 Â Â 9
4 - Â * Â Â 0 Â Â #
1 - Â M Â Â R Â Â B
   |   |   |
   2   20  5
Next wire up as follows:-
Keypad  >   Arduino
9 Â Â Â Â > Â Â D2
8 Â Â Â Â > Â Â D3
6 Â Â Â Â > Â Â D4
4 Â Â Â Â > Â Â D5
1 Â Â Â Â > Â Â D6
2 Â Â Â Â > Â Â D7
20 Â Â Â > Â Â D8 Â + (Remember, 20 is keypad pins 10, 7 & 3 joined together to make a single column)
5 Â Â Â Â > Â Â D9
Then
const byte ROWS = 5; //five rows
const byte COLS = 3; //three columns
char keys[ROWS][COLS] = {
 {'1','2','3'},
 {'4','5','6'},
 {'7','8','9'},
 {'*','0','#'},
 {'M','R','B'}
};
byte rowPins[ROWS] = {2, 3, 4, 5, 6}; //connect to the row pinouts of the keypad
byte colPins[COLS] = {7, 8, 9}; //connect to the column pinouts of the keypad (20 is 3,7 & 10 joined together)
Let me know if that works.
The handy thing is, this is still 8 pins, so you could wire this to an 8 bit I/O expander such as PCF8574 if you wanted to convert over to Keypad_I2C to do it all on 2 Arduino pins.