Another source for you is the The Complete Military Medal Medal Rll 1914-19 by Peter Warrinton 2019 (Naval and Military Press). Vol 3 page 364 lists the following info:
Carroll, James Wilson, mm, 3/12492, Pte, 2nd West Riding Regiment, also served with 9th Battalion//LG 31469 / 23.7.19. => London Gazette issue 31469 dated 23 Jul 1919. You should be able to find him listed here. Hope this is additional information and of value as well.
Please note that the Military Medal was normally awarded to Commonwealth (Imperial) personnel. Was awarded to American Army personnel as well.