Captured CS flags during the war were supposed to go to the War Department but the further away from Washington you were the less likely that happened.
Union states then were also somewhat enamored with "states rights" and since their troops were volunteers, many flags were sent to the state governors of some other prominent elected official or businessman who helped raise a certain regiment. Other CS flags were simply "sent home" to the families of officers.
We estimate that there are over 200 CS flags still up North, about half in museums. The number may even be bigger than that. None of the 18 flags taken at Corinth in October, 1862 made it to the WD, nor did any of the 85 claimed Vicksburg flags. None of the Donelson flags captures did either. I know from the Cincinnati Sanitary Fair of December, 1863, that two Vicksburg flags were loaned to the fair from Union Gen. Frank Blair, a Texas and Louisiana flag. They are still probably with his descendants. One of the CS flags taken at Helena in July, 1863 was sent to the St. Louis Merchant's Exchange as they helped raise the regiment. Where that one is now I have no clue.
Thus, the flags that Iowa has were taken by Iowa troops and sent to the state during the war. The Federal government has no hold over these captured colors and they were not affected at all by the 1905 return of CS flags from the War Department to the various Southern states and the antecedent organization of the MOC.
Having seen the collection in Iowa I can assure you that they treat them as reverently as they do their own flags and they are properly stored in state of the art facilities under proper climate controls. In fact, they have better facilities than at least one prominent Southern museum I know of (not the MOC).
It is up to Iowa of they want to return the flags. Some Northern states already have: Michigan, Wisconsin (although they have a few more still), Ohio (who still has two), etc. and these are only the state museums. Several other Ohio museums also have CS flags like the one in Massillon, Sandusky and the Rutherford B. Hayes Home.
Professional museums do make loans of flags and maybe some state museums will contact Iowa about this.
Regarding their collection a few notes from me:
200. 31st Alabama 1st National - has a Latin Cross in the canton - Champion's Hill capture
201. 37th Arkansas Polk - this is not a Polk Corps flag - but a variant of the Taylor pattern - blue with red Southern Cross. Another version of this flag also exists for another Arkansas (Dobbin's Cavalry)unit in that state's collection.
202. 40th Mississippi Van Dorn - captured at Corinth
203. 45th Alabama Hardee - captured in the Atlanta Campaign I believe
205. South Carolina Secession ? - This is a very large state flag taken in Columbia, SC if I correctly recall.
214. Unidentified (Dillard Grays #443) 2nd National - the Dillard Greys were a local Georgia defense company in Columbus, GA. This flag was taken during Wilson's Raid of 1865. They were presented the flag in mid-1863.