You dont even need to do that
The article very clearly states that the device is powered by a bio-battery.
Your stomach acid is 0.05% Hydrochloric Acid among other things, which is perfectly capable of eating small quantities of metal. Being as Magnesium and Copper turn into oxides (and are useful minerals in the body) at different speeds, power is generated just like in a potato/lemon/etc battery and used by the device.
Speaking from experience, I've made a few tiny batteries using magnesium and copper, and they dont last long even when used as skin-contact cells. (Yes, I DID invent wearable batteries that use sweat as electrolyte!) I'd estimate 1.4V at 0.1mA total power for maybe a few days, probably nearer 48 hours inside my body, and I use a *lot* more magnesium than would fit into a milliscale device.
Basically there'd be nothing left to dispose of, or worry about remaining inside.