What should you do when a user turns in a tablet computer with a swollen battery?

Make sure the device is not plugged into a charger and immediately turn the device off if the battery is swollen. It might be possible to remove the battery, but since the casing is already compromised, swollen batteries are more likely to explode than normal ones; and most batteries in small devices are not user-replaceable. Buying a new device is the best course of action.
To properly dispose of the battery or device, bring it to a recycling center. Never merely toss it in the garbage since it might explode, endangering sanitation workers and causing serious environmental harm.