In embodiments a WCD system is worn and/or carried by an ambulatory patient. The WCD system analyzes an ECG signal of the patient, to determine whether or not the patient should be given an electric shock to restart their heart. If so, then the WCD system first gives a preliminary alarm to the patient, asking them to prove they are alive if they are. The WCD system further determines whether the ECG signal contains too much High Amplitude (H-A) noise, which can distort the analysis of the ECG signal. If too much H-A noise is detected for a long time, the WCD system may eventually alert the patient about their activity, so that the ECG noise may be abated. The WCD system may even pause the analysis of the ECG signal, so that there will be no preliminary alarms that could be false until the ECG noise is abated.