If you don't have the tool, you can use a flathead screwdriver. Insert the tool or screwdriver into the hole at the top of the doorbell, then pull the doorbell up and away from the wall. I don't have the battery version so not sure if it is tricky to remove or not.
Here is the Nest Doorbell help page for some more info: Install Nest Doorbell (battery) - Android - Google Nest Help
There may be some Youtube videos with removal clips so that could be helpful to search as well.