Answer:
There are two ways to prevent the battery from leaking to the input side of the controller or to the power source or the circuit:
1. Consider adding a block PFET to the circuit, as this can help reduce the leakage voltage. When the battery is the sole power source, this PFET also helps in reducing battery drain current caused by any load at VIN, which is conducted through the body diode of the topside power switch on the LTC4121.
2. Alternatively, placing a diode between the solar panel or power source and the LTC4121 Input pin can also resolve the issue, although it may result in some efficiency loss.
Datasheet page 25: