If an insect falls into a cup of tea and is floating on top, some permit removing it on its own. Others are stringent and maintain that removing the bug on its own is Borer, because it is considered psolet that is being removed from okhel. It is proper to be stringent and remove the bug with a spoon in such a way that some liquid is removed with it. Alternatively, one can tilt the cup and pour off some tea together with the bug.
This also applies if a bug fell into soup or food. One may remove it with some of the food using a spoon. However, if multiple bugs fell into the soup or food, one may not remove them with a bit of food. This is because it is clear that what one actually intends is to remove the psolet, and therefore the okhel in the spoon is secondary to the bug. Since one is separating psolet from okhel, he is transgressing the prohibition of Borer. The way to get around this problem is to remove a large amount of food together with each bug, such as by using a cup, so that the majority of what is being removed is okhel. Then it is considered separating okhel from okhel, which is permitted.
One may rinse off fruits that have dirt on their peels for immediate consumption. However, one may not soak the fruit in water so that the dirt separates and sinks to the bottom.
. Thus states Taz 506:3; MB 319:61; Ben Ish Ĥai, Year 2, Beshalaĥ 13; and additional Aĥaronim. R. Shneur Zalman of Liadi writes in his siddur writes that removing a bug might obligate a person to bring a sin offering (that is, it violates a Torah prohibition). In contrast, some are lenient and allow the bug to be removed by hand, either because a bug floating on top of water is not considered mixed (Mahari Ĥagiz) or because the prohibition of Borer for liquids only applies to using a strainer, and not to separating by hand (Responsa Maharitatz Yeshanot §203). Menuĥat Ahava 2:7 n. 106 and Yalkut Yosef 319:28 cite them at length, but nevertheless add that in practice it is preferable to remove the bug together with a little liquid using a spoon.. See SSK ch. 3 n. 41 and ch. 5 n. 24 and Shulĥan Shlomo 319:43, which cite the following in the name of R. Shlomo Zalman Auerbach: One may not remove multiple bugs mixed into soup, even if one removes them together with a bit of soup. This is because even when it is just one bug, R. Shneur Zalman of Liadi in his siddur says one might violate a Torah prohibition. To be sure, many Aĥaronim maintain that the prohibition of Borer is not relevant here because the bug is floating on top and is not mixed in with the food. But if there are many bugs, then it is considered a mixture of okhel and psolet; thus, one who removes the bugs, even just using a spoon, is clearly focused on removing the psolet. That is all according to R. Shlomo Zalman Auerbach. It is reasonable that if one removes a lot of food with each bug, then this is not considered removing psolet from okhel but rather removing psolet together with okhel.
. Shabbat 140a states that one may not soak cresses in order to remove the psolet stuck to them. This is recorded in SA 319:8. MB ad loc. 28-29 extends this law to other fruits and vegetables as well. According to BHL, this is prohibited by Torah law, while according to Pri Megadim (Mishbetzot Zahav 5) it is rabbinic, since it involves a shinui. As a result of this, some prohibit washing off fruits (Minĥat Yitzĥak §38, which adds that minimally one should wash them with a shinui). Others prohibit washing many pieces of fruit (see Shevet Ha-Levi 1:52; Az Nidberu 1:15 and 8:6-7). However, most poskim maintain that there is no prohibition on washing fruit, either because there is no prohibition of Borer here at all, or because this is the normal way to eat. If the second reason is correct, then one may wash the fruit only for fairly immediate consumption. This is indeed the approach of Ketzot Ha-shulĥan §125, Badei Ha-shulĥan §16; Igrot Moshe OĤ 1:125; Tzitz Eliezer 6:37; SSK 3:22; Livyat Ĥen §52; Menuĥat Ahava 2:7:20.