[kronckew]

US Armed forces are governed by the UCMJ - Uniform Code of MIlitary Justice.

From a JAG (Judge Advocate General) Text

WAR TROPHIES.
A. Captured Or Abandoned Property. UCMJ art. 103.
1. Soldiers must give notice and turn over to the proper authorities without delay
all captured or abandoned enemy property.
2. Soldiers can be punished for:
a) Failing to carry out duties described in ¶ 1 above.
b) Buying, selling, trading or in any way disposing of captured or
abandoned public or private property.
c) Engaging in looting or pillaging.

JAG Linky

Case law: (sets precidents)

...a) Wrongful taking. Requires dominion, control, and asportation. See generally
United States v. Carter, 24 M.J. 280 (C.M.A. 1987); United States v. Smith, 33 M.J. 527 (A.F.C.M.R. 1991), aff’d, 35 M.J. 138 (C.M.A. 1992); United States v. Pacheco, 56 M.J. 1 (C.A.A.F. 2001) (stealing war trophies). The taking, obtaining or withholding is wrongful if done without the knowing consent of the owner or other lawful authority. MCM, pt. IV, ¶ 46c(1)(d).

(1) United States v. Sneed, 38 C.M.R. 249 (C.M.A. 1968). Where
accused’s accomplices were government agents, larceny of government
property could not stand as no taking ever occurred, i.e., articles were
never out of government control. See United States v. Cosby, 14 M.J. 3
(C.M.A. 1982) (accused can be guilty of wrongful taking even though
property was released to him by competent authority); see also United
States v. Cassey, 34 C.M.R. 338 (C.M.A. 1964) (OSI authorized
accomplices to proceed with delivery of government property and then
apprehended accused after delivery as he attempted to leave base).

however, for specific orders relating to iraq:

...
F. War Trophies/Souvenirs. The LOW authorizes the confiscation of enemy military property. War trophies or souvenirs taken from enemy military property are legal under the LOW. War trophy personal retention
by an individual soldier is restricted under U.S. domestic law. Confiscated enemy military property is property of the United States. The property becomes a war trophy, and capable of legal retention by an individual Soldier as a souvenir, only as authorized by higher authority. Pillage, that is, the unauthorized taking of private or personal property for personal gain or use, is expressly prohibited.

1. War Trophy Policy. 10 U.S.C. § 2579 requires that all enemy material captured or found abandoned shall be turned in to “appropriate” personnel. The law, which directs the promulgation of an implementing directive
and service regulations, contemplates that members of the armed forces may request enemy items as souvenirs. The request would be reviewed by an officer who shall act on the request “consistent with military customs, traditions, and regulations.” The law authorizes the retention of captured weapons as souvenirs if rendered unserviceable and approved jointly by DoD and the Bureau of Alcohol, Tobacco, and Firearms (BATF).

Implementing directives have
not been promulgated.

2. Guidance. USCENTCOM General Order Number 1 is perhaps the classic example of a war trophy order. These regulations and policies, and relevant UCMJ provisions must be made known to U.S. forces prior to combat. War trophy regulations must be emphasized early and often, for even those who are aware of the regulations may be tempted to disregard them if they see others doing so.
a. An 11 February 2004 Deputy Secretary of Defense memorandum establishes interim guidance on the collection of war souvenirs for the duration of OPERATION IRAQI FREEDOM (OIF) and will remain in effect
until an updated DoD Directive is implemented. This memorandum provides the following:
(1) War souvenirs shall be permitted by this interim guidance only if they are acquired and retained in accordance with the LOW obligations of the United States. Law of war violations should be prevented and, if committed by U.S. persons, promptly reported, thoroughly investigated, and, where appropriate, remedied by corrective action.
(2) All U.S. military personnel and civilians subject to this policy, operating in the Iraqi theater of operations during OIF shall turn over to officials designated by CDRUSCENTCOM all captured, found abandoned,
or otherwise acquired material, and may not, except in accordance with this interim guidance, take from the Iraqi theater of operations as a souvenir any item captured, found abandoned, or otherwise acquired.
(3) An individual who desires to retain as a war souvenir an item acquired in the Iraqi theater of operations shall request to have the item returned to them as a war souvenir at the time it is turned over to persons
designated by CDRUSCENTCOM. Such a request shall be in writing, identify the item, and explain how it was acquired.
(4) The guidance defines “War Souvenir” as any item of enemy public or private property utilized as war material (i.e., military accouterments) acquired in the Iraqi area of operations during OIF and authorized to be retained by an individual pursuant to this memorandum. War souvenirs are limited to the following items: (1) helmets and head coverings; (2) uniforms and uniform items such as insignia and patches; (3) canteens,
compasses, rucksacks, pouches, and load-bearing equipment; (4) flags (not otherwise prohibited by 10 U.S.C. 4714 and 7216); (5) knives or bayonets, other than those defined as weaponry [in paragraph 3 below]; (6) military training manuals, books, and pamphlets; (7) posters, placards, and photographs; (8) currency of the former regime; or (9) other similar items that clearly pose no safety or health risk, and are not otherwise prohibited by law or regulation.

Under this interim guidance, a war souvenir does not include weaponry.

(5) Acquired. A war souvenir is acquired if it is captured, found abandoned, or obtained by any other lawful means. “Abandoned” for purposes of this interim guidance means property left behind by the enemy.
(6) Weaponry. For this guidance, weaponry includes, but is not limited to: weapons; weapons systems; firearms; ammunition; cartridge casings (“brass”); explosives of any type; switchblade knives; knives with
an automatic blade opener including knives in which the blade snaps forth from the grip (a) on pressing a button or lever or on releasing a catch with which the blade can be locked (spring knife), (b) by weight or by swinging motion and is locked automatically (gravity knife), or (c) by any operation, alone or in combination, of gravity or spring mechanism and can be locked; club-type hand weapons (for example, blackjacks, brass knuckles, nunchaku); and blades that are (a) particularly equipped to be collapsed, telescoped or shortened, (b) stripped beyond the normal extent required for hunting or sporting, or (c) concealed in other devices (for example, walking sticks, umbrellas, tubes). This definition applies whether an item is, in whole or in part, militarized or demilitarized, standing alone or
incorporated into other items (e.g., plaques or frames).
(7) Prohibited Items. For the purposes of this interim guidance, prohibited items include weaponry and personal items belonging to enemy combatants or civilians including, but not limited to: letters,
family pictures, identification cards, and “dog tags.”
(8) See also MNC-I General Order #1, contained as an appendix to the Criminal Law chapter.

in other words, clear as mud. it does appear to allow 'confiscated' knives like the one shown, if turned over to the expressly designated authorities and a written request for the retention by the serviceman is filed at the time of turning over & approved by the authority.

never having been in this position myself, i don't know what forms, approvals and documentation would be generated. i'd assume that for a valuable antique such as this that permission to retain would be hard to get & a well documented paper trail would go with it.

reminds me of all the gold weaponry in saddam's various private arsenals.