Those rifles with the "mum" overstamped (usually with a circle) are surplus guns that were transferred to schools (college level). In pre-WWII Japan, military training was required in all schools from the primary grades through college. The smaller children used sticks or wooden rifles; the high school level used those rifles we call "training rifles" that fired blanks. College level students graduated to firing live ammunition from real rifles. Since the Type 38 was made obsolescent by the adoption of the Type 99, many were transferred to the college level training program. Since they were no longer in Imperial service, the Emperor's family "mon", the chrysanthemum, was overstamped. (The same idea is shown by the British "double broad arrow", which looks like an asterisk.)
Watch those "Arisakas" without a Type marking and with one piece stocks; those are two of the signs of training rifles, some of which are thought by collectors to be "variations" of the Type 99 or Type 38. One was offered to me not long ago at a high price as an "experimental" rifle because of the low serial number and lack of markings.