Short answer: you may need to install a resistor (recommended 10Ω(Ohm) 0.5W) across the terminal screws on your mechanical doorbell. See below for example:
Long explanation: It is not uncommon to hear the chime buzz after installing a video doorbell. The reason is that before you installed Sentry, the doorbell button acted as a switch for the electric circuit, so when the button was pressed, the circuit was closed and the chime rang. Sentry video doorbell requires constant power, so the circuit is always closed. Depending on the power consumption of the chime, there might be enough residual current in the circuit to cause the chime to buzz. Installing a resistor across the terminal screws dissipates the current through the chime, thus reducing the buzzing sound.