According to the Gemara, if fish was cooked in a pan that had been used for meat, nevertheless the fish can be eaten with kutah (a type of dip made of milk ingredients). In contrast, if a tznon (=radish) was cut with a meat knife it may not be eaten with kutah. This is so only in the case of a radish,which, on account of its strong flavor, absorbs from the knife, but in the case of kishut (= cucumber) one need only scrape away the surface of the cut and then one may eat it with kutah. Lifta (=turnip stalks) are permitted; silka (=beet stalks) are forbidden, but if one cut these and turnips alternately, they are permitted.
When there is no actual meat – just the taste of meat that was absorbed by the pot or pan – only a secondary taste would be transferred to the fish that is cooked. That taste is referred to as noten ta’am bar noten ta’am – something that gives taste which is the progeny of something that gives taste. When the source of the taste is something permissible, we do not view that as significant. Regarding the case of the sharp vegetables, Rashi offers two explanations for why we are stricter when they are cut with a meat knife. First of all, we must assume that a knife used for meat will always have some oily remnants from that meat that may not be visible, but would affect the flavor of the vegetable. Additionally, the pressure applied when cutting into the vegetable may force the taste absorbed in the knife into it. Tosafot add that this would apply to all sharp vegetables, including onions, leeks and garlic.
Kutah ha-Bavli was a dip that was prepared for people to eat together with their bread. It was popular in Bavel (which is why it is called kutah ha-Bavli ) and was made from moldy bread mixed with whey and salt.