When words pass from one language or country to another, you will usually find that the pronunciation changes to suit the new language. Words may even be subject to changes in pronunciation within the same language over time, which often obscure the original meaning (consider the change to "daisy" from the original "day's eye (dæges eage)" in English). An interesting case of this in Korean is the word "양치(질)," meaning "to brush one's teeth."
In the historical text 계림유사 (12th century), the pronunciation is indicated as "養支 (양지)." Spelled with its original Hanja (Chinese characters) the word is 楊枝 (양지), which literally translates to "willow tree branch." At the time, willow tree branches were used as a substitute for our modern toothbrushes, as can be seen at 1:30 in the following video. According to the video, willow tree branches were used because they disinfect your mouth and help stop toothaches:
As the original meaning of the word grew less clear over time, it was influenced by the Chinese characters "養齒 (양치)," meaning "to take care of one's teeth," which changed the pronunciation of the word to the modern form 양치 and obscured the original sense of the word.
The word "양지 (楊枝)" crossed over to Japan and was pronounced "요지 (yoji) but instead meant "toothpick". (Even now, yoji, or "ようじ (楊枝) is the Japanese word for toothpick.) At some point in time, very likely during Japan's occupation of Korea, the word "요지" returned and can still be found in dialects of Korean to this day where, as in Japanese, it means "toothpick" as opposed to "brushing one's teeth."
백문식. 우리말 어원 사전. 1st ed. 서울: 도서출판 박이정, 2014. Print.