ㄷ at the beginning of a word most likely sounds closer to the Japanese "t" to Korean speakers than ㅌ does.
Why it sounds closer needs a more technical explanation:
In general, "t" and "d" are very similar sounds (also the pairs "p"/"b" and "k"/"g"). They're pronounced in the same place in the mouth and they both briefly stop the flow of air, but not all languages distinguish them in the same way. There are two main ways, which linguists call voicing (vibration of the vocal cords in the throat) and aspiration (a puff of air after the sound).
As I understand it, ㄷ at the beginning of a word is unvoiced and unaspirated, while ㅌ is unvoiced and heavily aspirated. For Japanese, "d" is voiced and unaspirated, while "t" is unvoiced and slightly aspirated. That means ㄷ is quite similar to a Japanese "d". Between voiced sounds (like vowels), ㄷ is voiced and sounds more like the Japanese "d", so ㅌ sounds closer to the Japanese "t" in the middle of a word.
There are quite a few Japanese place names which are like this in Korean. For example, Kyoto is 교토 (Gyoto), Kobe is 고베 (Gobe), Toyama is 도야마 (Doyama), Kumamoto is 구마모토 (Gumamoto), Tokushima is 도쿠시마 (Dokusima).