LDO Regulator TPS737xx, connecting Enable to VIN and avoid damage when removing VIN
It basically tells you that when EN is connected to VIN, it may happen that current flows from the output towards the input, after VIN has been removed. Or/and that upon power-up the ramp up time of the output may be faster than usual.

This is due to the fact that the gate of the MOSFET that is the switching element (in broad terms it is inserted in-series between the input and the output) may maintain some charge, with the result that the MOSFET is still conducting. That's why this reverse current may be observed and the ramp up time may be faster.

The correct way to do it in order to avoid such a case, if you had the EN connected separately from VIN, would be to first drive the EN low to discharge the gate capacitance of the MOSFET and then remove VIN.

There is actually no real risk for the LDO itself or your battery, since it is anyway removed. It's just something they mention because it could be undesirable for some applications. I believe you shouldn't worry about this.