Under normal circumstances charging a phone with a power bank will not damage the battery. In fact, it should have the same effect as charging your phone via its conventional charger.
For the phone, it does not matter which power source you use as long as the current is within the admissible limits. You can even charge the phone directly via solar panels as long as the power is stable and has the right values. Smartphones require a 5V input to get charged. So as long as the device you’re charging them with delivers that output, you don’t need to worry.
Power banks deliver at least 5V of power, but in some cases, they can deliver more than 5V too. For example, some power bank models can deliver up to 20V if needed as in the case of charging laptops. But even if the power bank can deliver more than 5V of power, you still shouldn’t worry as both the power bank and the phone have power regulating circuits, that allow the mobile to only take 5V and not more. However, should the charging regulating circuit fail, then you could indeed see a negative impact on the phone’s battery.
Think of the power bank as a tank or reservoir from which the smartphone can draw power. The power reservoir cannot forcefully feed power to the phone. Thus you need not worry that power banks damage your battery.