I believe horseradish stays contained as long as you don't break the
roots. It will become a strong healthy looking plant but shouldn't take over or spread. I'd leave it be. If you want to harvest horseradish
root from it, maybe do that once and plant some of the root bits somewhere where you don't mind the risk of multiplying as you harvest each year.
There is a lady in my garden club who's helpful son rototilled her garden AND her horseradish patch. Now she has it everywhere.