High voltage in electrical grid and Inverter's voltage output range
I assume that the inverter is also a battery charger, and will charge the batteries when grid power is available, as well as passing grid power to the connected load.

If that is the case, it is quite reasonable for the inverter to pass whatever voltage it receives to the load.  The load is no more likley to be damaged by high voltage than if it was connected directly to the grid.

If you had given the inverter make and model, I would have been able to confirm my assumptions.