If the running water noise continues once the tank is filled you may want to call a professional plumber to investigate the situation for you.
Tankless water heater noisy pipes.
Or you can try to run down the leak yourself by checking the following.
Good luck with your project.
Another common problem that can create noise in tankless water heaters is a dirty flow sensor which controls how much gas is sent to the unit.
Other sources of noise include blocked or inadequate ventilation or a defective or improperly set pressure valve.
In that case you need to have a plumber install a check valve in the water line.
If you hear a weird groaning sound from the pipes or the tankless hot water heater when you flush the toilet that could be the culprit.
Generally speaking there is a lower chance of hearing strange noises with a tankless water heater vs tank model.
Even though a toilet only uses cold water i have seen some toilets do this.
Others reasons for a noisy tankless water heater model may be an issue with the burner the fan may be dirty or possibly a leak in the sealed combustion resulting in irregular gas combustion.
Water vapor is a byproduct of combustion although in this case the vapor contains elements such as methane nitrogen and oxygen.
A blocked or improper ventilation and even a defective or wrongfully set pressure valve can also make your tankless water heater loud.
Although keep in mind that it is normal to hear water entering the tank when hot water is being drawn.
Another standard issue that causes loud noises in tankless water heaters is a dirty flow sensor.