>I'm curious why you wouldn't just bury the calcium carbonate pellets at this point

Potassium hydroxide absorbs carbon dioxide:

2 KOH + CO2 >> K2CO3 + H2O

Calcium oxide regenerates potassium hydroxide:

CaO + K2CO3 + H2O >> CaCO3 + 2 KOH

Calcium oxide is recovered by heating:

CaCO3 + heat >> CaO + CO2