Is 찻집 (a tearoom) a pure Korean word?

ANSWER: Yes. Since 2017, the National Institute of Korean Language has claimed that 찻집 is a pure Korean word. That means that they consider 찻집 to be the pure-Korean equivalent of the Sino-Korean word 다방 (茶房), which means "teahouse" or "tearoom." And that suggests that they also consider the correct pronunciation of the Chinese character 茶 to be just /다/, not both /다/ and /차/.

My 2014 edition Minjung's Essence Korean-English Dictionary, however, was published before the National Institute of Korean Language changed its mind on 찻집 and, therefore, lists 찻집 as a combination of the Chinese character for "tea" (茶) and the pure Korean word for "house" (집). That means that Minjung needs to update not only its definition of 찻집 (teahouse) but also its definitions of 찻감 (stuff to make tea out of), 찻물 (tea), 찻숟가락 (teaspoon), 찻잎 (tea leaves), 찻장 (a tea cabinet), and 찻종 (a teacup, a tea bowl) by removing the Chinese character 茶 that appears in the parentheses next to those words. So, the listing for 찻집 should be just "찻집," without parentheses, not "찻집 (茶 --)."

2014 edition of Minjung's Essence Korean-English Dictionary

By the way, there are only six 2-syllable Sino-Korean words that are officially allowed to use 사이시옷 in their spellings. A 사이시옷 is a ㅅ that is sometimes added to a syllable of a compound word to show that the last syllable of a compound word is pronounced differently than its spelling. Normally, the compound words that use 사이시옷s have to be either pure-Korean compound words or a combination of a pure-Korean word and a Chinese character. The six Sino-Korean words below are the only exceptions to that rule:

• 곳간 (庫間) a storeroom, a warehouse
• 셋방 (貰房) a room for rent, a rented room
• 숫자 (數字) a figure, a numeral
• 찻간 (車間) the inside of a train car, a railway carriage
• 툇간 (退間) the wooden floor verandah attached to a traditional Korean house
• 횟수 (回數) the number of times (something is done), frequency

Notice the 찻찬 (茶盞), 찻장 (茶欌), and 찻종 (茶鍾) that are shown in the above screenshot from my Essence dictionary are not in the above list. If the 찻 in those words was really a Chinese character, then the 사이시옷 in those words would not have been allowed in their spellings since they were then considered Sino-Korean words. But since the 사이시옷 was and is allowed in the spellings of those words, that is evidence that the 찻 in those words is really a pure-Korean word, not a Chinese character.