A multi-annual chart on the "trading economies website suggests Israeli arms exports have a "total insurable value" of hundreds of millions of USD per year.
This sentence contains anchor text for two links. One is explaining "total insurable value", which doesn't seem to be at all relevant, and based on you simply assuming that "TIV" stands for "total insurable value" in this context. The other is for a link that gives "606 SIPRI TIV Million in 2021" for Israel. I did ctrl-f on "USD" on that website, and got no results, so that seems to be just your mind filling things and treating it as part of the original source. After some googling SIPRI TIV, I got results such as these:
SIPRI has developed a unique pricing system to measure the volume of deliveries of major conventional weapons and components using a common unit—
the SIPRI trend-indicator value (TIV). The TIV of an item being delivered is
intended to reflect its military capability rather than its financial value. This
common unit can be used to measure trends in the flow of arms between particular countries and regions over time—in effect, a military capability price
index. Therefore, it is important to ensure that the pricing system remains consistent across both the weapon systems covered and over time, and that
any changes introduced are backdated.
In a Trade Register, deals are divided between, on the one hand, those that involve the physical transfer of military equipment and, on the other, those that involve the transfer of technology or provision of a licence, allowing the goods to be produced or assembled by the recipient.
Showing all international transfers of major conventional arms since 1950, The SIPRI Arms Transfers Database is the most extensive source of information on international arms transfers available to the public. The database is updated every spring and is useful for anyone seeking to monitor and measure the international flow of major conventional arms.
So, TIV is an abstract unit that SIPRI uses to measure arms sales. I again saw no mention of it being based on USD, and in fact SIPRI says that it is not "financial" value. They may have taken some currency as a starting point, but there isn't a one-to-one correspondence. Assuming that the base currency, if it exists, is USD is a bit US-centric, and even if it were, the desire that "the pricing system remains consistent across both the weapon systems covered and over time" implies that it is not adjusted for inflation. TIV tracks arms transfers since 1950. If they used 1950 USD as a starting point, then 606 corresponds to about 7.2 B in 2022 dollars.
Ha'aretz, an Israeli newspaper, reports that the 2021 sales reached 11.3 Billion USD.
That article says:
Last year set a record for the volume of Israel’s military and security exports, which surged by 30 percent over the prior year, according to the Defense Ministry’s International Defense Cooperation Directorate. Israeli defense industries reported new contracts worth a cumulative $11.3 billion in 2021 – up from $8.6 billion in 2020.
"Contracts" and "exports" are not the same thing. Arms deals often, if not most of the time, involve the sale of arms that haven't been built yet, sometimes even coming from factories that haven't been built yet. It can be years from order to delivery. Also, while this strongly implies this is the number for exports, it doesn't explicitly state that.
Also, that article is a bit confusing, as it says "2022" in a few places, and refers to the Ukrainian War. While Ukraine was invaded in 2014, the term "Ukrainian War" generally refers to events after the 2022 invasion.
Now, Israel's entire exports seem to be a little over 50 Billion USD, according to the Observatory on Economic Complexity (OEC).
It says that Israel's product exports are about 50 B, with services being around the same size. SPIRI says that arms exports include both "physical transfer of military equipment and ... the transfer of technology or provision of a licence, allowing the goods to be produced or assembled by the recipient." The latter could be considered service exports.
There does indeed seem to be discrepancies regarding reports of the size of Israel's arms exports, but I don't think it's due to people "cooking" the numbers.