My interpretation was that the actual mass of the bob doesn’t contribute to the period of the pendulum. I suppose it could shift the centre of mass somewhat relative to the mass of the rod?
The pendulum in the clock colloquially called Big Ben is regulated by adding or subtracting from a stack British pre-decimalisation one penny coins. However in this case they are placed at the top of the bob not at its centre of mass so adding a penny shortens the pendulum by moving the centre of mass of the bob up