I have a specialist collection of modern machine struck square coins, (82 different types so far).
For the Iraq 500 Fils, and 500 Falsan, Krause lists 2 main types:
1. Palm tree in 2 varieties -
KM#165, 9.08 grams
KM165a 500 Falsan, with reduced weight 8.9 grams.
2. Lion of Babylon in 2 varieties -
KM#168,
KM168a 500 Falsan, both 9.08 grams.
All were struck in pure nickel, attraction to a magnet confirms this.
The 500 Fils pictured appears to be KM#165.
Krause lists a proof set with KM168 (Lion of Babylon) for these, but the "500 Fals" (KM#165 Palm Tree) on the coin pictured, together with the form of card presentation, suggests that the set pictured is a mint set, not a proof set.
I have only one of each main type:
KM#165a, and KM#168. They came to me via Joel Anderson Coins, Ca.
I would guess that the carded mint sets were what were most commonly brought back from Iraq by American service personnel coin collectors.
Perhaps a few of the other varieties of the 500 Fals and 500 Falsan were brought back also, but as unused pocket change, and are most probably ignored by those families that may have them.