(It used to be easy to remove the battery...)
Indeed, but not any more. Starting with the Retina models, Apple glued the batteries in place. Removing one is "theoretically" an at-home job but requires a strong, flammable solvent to unstick the battery, You may also find the case is permanently deformed and you won't be able to fix that. If the chemicals get on certain parts of your computer, it can ruin them. Same with your skin and your lungs.
Best to ask Apple if they still will replace the battery in your model.
Mac Repair - Official Apple Support
Battery service does not appear to follow the usual guidelines for "vintage" products, a good thing in this case.
I cannot recommend using an Apple Authorized Service Provider for this. Too many cannot store or use the required chemicals in a commercial setting due to local fire codes. They can only replace the entire upper deck including keyboard, trackpad, and battery. That can triple the cost of an Apple battery swap. Only use an Apple Authorized Service Provider if they can confirm the US$129 pricing.