Thank you for the follow-up via email.

Here is the information that puts the flag being captured at Mobile. One of the people working to try identify exactly whose flag this was received it from the Iowa Flag Historian:

From the hospital bed of Willard Baker, Pvt. Co. C, 20th Iowa Infantry, University of Iowa Hospitals, Jan. 24 ,1919.

The other two flags I got at Mobile and were made of English bunting. . . “The Palmetto Flag carries the emblem of the State of South Carolina, but how the flag happened to get to Alabama, I do not know."

The description of the flag by the Iowa Historical Society has this:

C. Cat. # 41. Palmetto Flag: red wool bunting with palmetto tree in center in white cotton, white cotton crescent moon.
Captured at Mobile, Alabama by the 20th Iowa Volunteer Infantry, Co. C.