Katsuo ume is umeboshi paste mixed with katsuobushi (dried bonito flakes). When umeboshi is mixed with katsuobushi, the saltiness and sourness of umeboshi gets milder. If you happened to purchase too salty umeboshi, you can amend the flavor by mixing it with katsuobushi.
For instance, when you make noodle soup broth, good amount of soy sauce and mirin soaked katsuobushi is left behind. There is no reason to waste perfectly edible by-product. Finely chopped kombu after dashi is extracted also can be used.
Katsuo ume can be eaten simply with rice, just like the photo at the top. It is also used inside of onigiri or norimaki sushi roll.
You can make quick tasty morsels, which go well with sake by topping katsuo ume on cold tofu (the photo above left) or thin-skinned Persian cucumbers.
Katsuo ume can be kept in a refrigerator for months. It comes in handy when you keep it around.