Picard itself does not write any genre tag unless you have “Use folksonomy tags as genres” enabled. If this is off, it must be a plugin. Which ones do you have enabled? Try disabling them all.
Last possibility is that the tags are already present in the files. Have a look at the original tag value in the bottom left, is genre already set there? If so you can either manually remove it or you activate the “Clear existing tags” option. Be careful with the last one, it removes all the tags including cover art and only saves again what Picard provides.