Here is what Booth's records state:

McGrew, James C., Pvt. Co. K, 31st La. Inf. En. Monroe, La., April 14, 1862. Roll Jan. and Feb., 1863, Present. Federal Rolls of Prisoners of War, Captured and Paroled Vicksburg, Miss., July 4, 1863. On List dated Hdqrs. Allen's Brig., Shreveport, La., March 29, 1864, reported in camp for exchange at Vienna, La., before April 1, 1864. On Roll of Prisoners of War, C. S. A., paroled Monroe, La., June 9, 1865. Res. Ouachita Par., La.

You may wish to see if there is additional information, such as his records on file with NARA

JIMT