If they are sending a new one, you always send back whatever you received new to being with, unless they specify otherwise. The battery is removable, but it's considered part of the device.
The battery is removable, but the new one did not ship with the battery in the device.
It's been over a year since I bought the original one. In truth, I have two extra batteries, so this would be a 4th battery, so it's not as though I need the thing. However, if they are just going to recycle it (i.e. in toxic waste dump), why shouldn't I keep it? There's an argument for it being dangerous to even ship the thing, it is toxic, plus li-ion batteries are known to explode in certain conditions, not likely, but am I the one to figure that out? Why shouldn't I just keep it?
Am I to remember if it came with a USB cable and charger after a year? I think it did, the new one did, but I am not sure where the original ones are, TBH.
I don't believe I'll get charged for the replacement phone because I failed to include the old battery. It is Amazon after all, and in my experience they are accommodating to their customers.
I'm really on the fence about this.