It is feasible to estimate a lower bound for how much greenhouse gas is produced by boiling water:
– 600,000,000 people rely on water which has been treating by boiling
– each person requires at least one gallon of treated water per day
– the heat for boiling the water comes predominantly from combustion of carbon-based fuels, typified by burning wood or charcoal
– as calculated in a previous post, 1268 kJ of heat energy is required to raise the temperature of a gallon of water from room temperature to boiling
– a cord of green firewood weighs about 4000 lbs ; a cord of seasoned firewood weighs about 2500 lbs
– when seasoned, a cord of firewood can be burned to produce about 20 million BTUs of heat energy
– each carbon atom (atomic weight 12) which is oxidized by burning a biomass fuel goes into a molecule of carbon dioxide (molecular weight 44 = 12 for the carbon atom + 2 * 16 for the two oxygen atoms)
– when dry, wood is about half carbon by weight

How much CO2 is produced by burning wood to boil a gallon of water? A lower bound for that number is the amount associated with combustion to produce 1268 kJ. Each BTU is equivalent to 1.005 kJ .
1268 kJ / (1.005 kJ/1 BTU) = 1262 BTU to heat 1 gallon of water to boiling
20,000,000 BTU / 2500 lbs = 8000 BTU per pound of seasoned firewood
(1262 BTU/gal ) / (8000 BTU/lb) = 0.16 lbs of seasoned firewood per gallon
0.16 lbs x 50% carbon = 0.08 lbs carbon
0.08 lbs carbon x (44 MW of CO2 / 12 AW of C) = 0.29 lbs CO2
So a lower bound for the amount of CO2 produced by burning biomass to boil one gallon of water is 0.29 lbs of CO2.

How many metric tons of CO2 are produced each year by boiling water for 600,000,000 people?
600,000,000 people x 1 gal/day x 365 days/yr = 219 billion gals/yr
219 billion gals/yr x 0.29 lbs CO2 x (0.45 kg/1 lb) = 30 billion kg of CO2
30 billion kg CO2 x (1 metric ton/1000 kg) = 30 million metric tons of CO2

At least 30 million metric tons of CO2 is produced each year by burning biomass to boil water. This figure accounts only for the heat required to raise the temperature of the water from room temperature to the boiling point. It does not account for the heat from the fire that doesn’t go to warming up the water, nor for the heat required to maintain the water at a boil for the duration of boiling treatment.