The implementation of such a system doesn't even need to send energy back to the grid at all - simply by having your batteries kick in to power your own load when they would otherwise maintain a reserve you are in effect providing power to the grid (that you would otherwise be drawing). The power is coming from literally inside your house, reducing the amount of energy that must be transmitted to your house from the grid.

It actually mostly just stays in your local area. You are effectively providing power to your neighbors. Some neighborhoods providing too much excess power back to the grid with solar panels is actually a challenge for grid operators currently. They simply don't have enough cable capacity. So, having a lot of batteries in the area helps them on that front because the power can be dumped there and then extracted when they actually need it.

Efficiency will always drop any time energy is converted between forms or transmitted.

The point is not to be efficient, it's to ensure the power is available when needed.

You more-or-less can't charge your battery from the grid (except in emergencies, subject to local regulations, etc.), so it's not sending the energy back and forth.

Our system seems to discharge 20% fewer watt hours than it spends charging the batteries.

As for transmission losses, you are likely powering houses on the same block as you, so they're hopefully mostly negligible compared to the battery charge/discharge loss.

In an event like this, you are effectively helping to power the other houses in your neighborhood. So it is likely to be fairly efficient.

I’d bet on ~95% round trip efficiency, if not more - lithium batteries are very efficient, as are modern power electronics.