Just running from that article (emphasis mine):
Knowing how much hydrogen had disappeared from the oceans over the
last four billion years enabled the researchers to calculate that the
oceans have lost about a quarter of their water since the Earth’s
"Hydrogen and deuterium are still escaping into space, but very
slowly, says Pope.
“Today the atmosphere is rich in oxygen, which reacts with both
hydrogen and deuterium to recreate water, which falls back to the
Earth's surface. So the vast bulk of the water on Earth is held in a
closed system that prevents the planet from gradually drying out."
The earth is estimated to be 4.5 billion years old. If it lost a quarter of its water since then, then the first order estimate is that we need another 13.5 billion years before the rest goes away. However, the rest of the quote suggests that the rate of loss has gone down dramatically in the last few billion years. Between that and the fact that such losses are proportional to the quantity of water around, I'd expect it to last much longer than that.
On that timescale, we have to ask questions about other issues we may have besides water rationing. For example, it is believed that, in 4-5 billion years or so, the sun is going leave the main sequence phase and progress towards becoming a red giant. During that transition, it is believed the Earth may, in fact, be swallowed up by the sun as its radius balloons massively.
So no.... reducing CO2 emissions for the next 100 years (or should I say 0.0000001 billion years to keep with the units of time used in the previous paragraph) is not going to have all that big of an effect, in the greater scheme of things.