The fact the US military probably pollute in other ways isn't really that relevant to the direct effects of Israel's war in Gaza though.

Here's a quick example of the kind of things people are looking at (this estimate doesn't look at things like forever chemicals and rebuild costs so it's quite a low estimate):

The vast majority (over 99%) of the 281,000 metric tonnes of carbon dioxide (CO2 equivalent) estimated to have been generated in the first 60 days following the 7 October Hamas attack can be attributed to Israel’s aerial bombardment and ground invasion of Gaza, according to a first-of-its-kind analysis by researchers in the UK and US.

According to the study, which is based on only a handful of carbon-intensive activities and is therefore probably a significant underestimate, the climate cost of the first 60 days of Israel’s military response was equivalent to burning at least 150,000 tonnes of coal.

The analysis, which is yet to be peer reviewed, includes CO2 from aircraft missions, tanks and fuel from other vehicles, as well as emissions generated by making and exploding the bombs, artillery and rockets. It does not include other planet-warming gases such as methane.

https://www.theguardian.com/world/2024/jan/09/emissions-gaza-israel-hamas-war-climate-change