@lylewiescamp use one of those thin spatulas you can get at the department store. Something that has the blunt edge on the front and is fairly flexible. I like the ones for the Tefal coated pots and pants :-) Get a syringe and inject some isopropyl alcohol (go with the higher percentage like nothing less than 90% and inject it between the battery and the case. Bit at a time and don't be overzealous. Haste makes waste.
Do this is in a fairly well ventilated room and just keep a bucket of sand or a fire suppression blanket available. Since you did not tell us if there is still a charge on the battery, we could assume that puncturing it could cause it to "vent with flame". It is very, very rare. Yes, you may get smoke and stink but not always a flame. Really, just use common sense.
You got this! Repair is War on Entropy