My koi fish ate a piece of gum

If the water is cold then it can be a problem, chewing gum will start to get soft at temperatures above 20 °C.

So if the water is warmer than 20 °C it will pass through your fish - slowly, but it will pass. The warmer the water, the faster it goes.

If your water is cold you might have a problem, but not always as the fish are able to regurgitate and spit it out

I have seen koi eat and spit out objects that have been in my pond, like styrofoam and plastic pieces, sometimes after quite some time.

Your koi are large, so I do not think they will have any problems passing the gum.