Tevul Yom, Chapter 4, Mishnah 2. This mishnah continues the chapter's concern with produce that is susceptible to tumah, and with the special standing of a tevul yom: a person who had been tamei, immersed in a mikveh, and is now waiting for the day to end before his taharah is complete. He is no longer simply tamei, yet not yet fully tahor, and the halachah has to decide what his touch accomplishes.
The case: "ochel ma'aser shehuchshar bemashkeh", a Levi is eating ma'aser produce that had already come into contact with a liquid and had therefore become susceptible to receiving tumah. Then "venaga bo tevul yom, o yadayim meso'avos", either a tevul yom touched that food, or it was touched by a person whose hands were unclean. One further detail is essential: terumas ma'aser had not yet been taken from this produce. A Levi who receives ma'aser is obligated to separate a portion of it, terumas ma'aser, and give it to a kohen. Here he is eating from the ma'aser while that obligation is still outstanding, and now the produce has been touched.
What does the halachah say? "mafrishin mimenu terumas ma'aser betaharah": he goes ahead and takes terumas ma'aser out of this produce as pure food, without any concern. The Mishnah spells out why. Its explanation begins "mipnei shehu shelishi": what a tevul yom, or hands that were not washed, transmit to this food leaves it holding a third-level tumah, a shelishi. And the rule attached to that level is "vashelishi tahor lechullin": with respect to ordinary, unconsecrated food, an item that is a shelishi carries no tumah at all and counts as tahor.
In practical terms, then, no loss has occurred. Being touched did not spoil anything, since at the degree of tumah this ma'aser now holds it simply is not reckoned as tamei for the matter at hand. So the Levi proceeds as he had intended: he takes off the portion of terumas ma'aser as pure produce and delivers it to a kohen, no differently than had no one ever laid a hand on the food.