Interesting point, why an apparently small effect from WW2.
The 1930s saw a very large Depression which might account for the slight drop in CO2 levels, and there is a vague hump that might be from the War. It's possible the measurements of the time were not themselves not sufficiently accurate and international for large but short-term, temporary changes to be very apparent. If any were taken, of course.
To some extent too, wartime use of fuel for non-important purposes would have dropped drastically, possibly off-setting some of the military uses and effects. WW2 was also followed in many countries by the "Austerity Years", again reducing fuel use.
It looks almost as if economic depressions had more effect than the wars and destruction.
What is particularly significant though is the overall rise, and its steepening in the 1960s, combined with the traces merging to show human activity having become the primary source of atmospheric CO2 overall since WW2.
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Ice-cores are a major source of palaeoclimate evidence. Another important one is cave deposits, by analysing sediments left by streams, and layers in calcite (stalagmite). Because caves take hundred of thousands of years to form, with some being possibly a few million years old, and their deeper conditions are fairly stable, they act as natural climate-evidence archives.