You could always try replacing the rusted terminals and solder new ones on, or you can clean them with rubbing alcohol and a q-tip, but since they are rusted, maybe use a toothbrush to scrape it off. I have seen battery compartments that look worse than that, and they are able to work again without disconnecting the power cables. There are many ways to clean battery acid. Corrosion is caused by a completely expected chemical reaction due to hydrogen gas building pressure and ultimately needing to escape from inside a battery.
# Apply baking soda over the entire area that's affected by corrosion. This will neutralize the battery acid. Add a small amount of water to activate the baking soda and cause a chemical reaction which will remove the corrosion. Clean and dry the area with a paper towel, and clean up any residue using a scrub sponge.
# Isopropyl alcohol is the best remedy for cleaning the corrosion of batteries. You should apply isopropyl alcohol on electronics because it is very safe to use. once you have applied, you need to rub it with a soft tissue or cloth.
# White vinegar or lemon juice: Most household batteries contain bases, so acids will neutralize their discharge.
# Hydrogen peroxide is an excellent cleaning agent for battery corrosion as it is an organic chemical. It is non-toxic if used correctly at the right doses. The mild oxidizer is safe to use with no toxic by-products. The chemical solution can overcome accumulated rust easily.
It is not recommended to use any chemical cleaners, such as bleach, ammonia or acetone as these can cause damage to the battery terminals. I know that 2012 furbys run on a 6 volt dc motor, therefore it would be 3 watts, 500mA for the power source. Usually, furbys only have 2 wires connecting on the battery terminals. the red and grey wires on the right are connected to separate metal connectors in the battery compartment, check the wires as they may have corrosion on them as well. Corrosion is easy to clean, but is time-consuming.
I hope this helps, Thanks!