Fifteen men from the Forest of Dean fought in the battle in April 1951, which was credited with saving South Korea’s capital, Seoul, from capture by Communist forces.
About 400 members of the Gloucestershire Regiment held out against 10,000 Chinese troops for three nights during the battle on hill 235, which was later renamed Gloster Hill.
The defacing of the plaque is believed to have happened over several days, and Gooch said the initial damage was done on Thursday.
“People are horrified and this is not a true reflection of the Forest as a whole,” Gooch said of the vandalism to the memorial, which was erected after £18,000 was raised in donations.
“[The arboretum] is a place of reflection, which was one of the reasons why that site was chosen.”