How to surpress coupling between two circuits
Addressing possible electromagnetic radiation from the transmitter:
Assuming that the received, unwanted pulse is coincident with the transmitted pulse, coupling would be speed-of-light electromagnetic coupling. Suppressing this radiation involves reducing the area of transient current in the MOSfet switch. An isolating inductor has been added to block AC current path from influencing +5V line:



simulate this circuit &ndash; Schematic created using CircuitLab
 A pull-up resistor is added for a different reason. Piezo internal parallel capacitance should be discharged between pulses, so that anode of D1 rises back up to +5V after the MOSfet becomes idle (open-circuit).

Note that taking these precautions may not solve the problem of coupling between transmitter and receiver circuits. The nasty path may be through ground, or too-open a layout of receiver circuitry. Too little information of OP's setup to address this  - a difficult one to deal with.