Ok, contrary to some opinions here, you cannot just leave a dead battery there and do nothing. Dead batteries still try to accept a charge so that means the motor generator will be trying to constantly trying to charge the dead battery, and that will end up using more fuel than if the battery wasn’t there to begin with.
In the Honda Civic, the hybrid system was a parallel system, meaning the engine, transmission and drive axles are conventional. An electric motor generator is sandwiched between the engine and the transmission or between the transmission and the drive shafts to add a little HP to the engine output while accelerating or going up steep hills. When coasting and braking, it recharges the battery. I think the additional HP is around 13, but at low gas engine RPM, that may be almost double what gas alone would provide.
When the battery dies, at the very least, you should have it disconnected. If you have it removed completely, that will remove some weight, but I don’t know how heavy this battery is or if it would be worth the trouble, but at least get it disconnected.
When the battery is disconnected, the terminals must be insulated and secured or they will short out causing other problems. It’s not just a matter of removing the wires.