Chosen Solution

I opened my MacBook Pro to swap the hard drive and noted the battery appears swollen. Is it safe to run like this? This computer is already plagued by the GPU failure so if the battery is now bad also, it’s probably time to recycle it.

Once the pressure of the bottom cover has been removed the battery may expand rapidly and become much more dangerous and difficult to remove, therefore DO IT NOW. Even if you do not have a tri-wing screw driver, many times the pressure has already broken the retainer tabs off. Sometimes you can use a small flat head driver to get them out or use a pair of dikes to just break or cut them. iFixit sells replacement batteries. gfxCardStatus software will allow you to turn off the integrated graphics feature of your GPU and continue to use the computer. https://gfx.io