I'm not familiar with the phrase "wet t" (and googling it was not helpful); I'm guessing it means palatalized. According to https://en.wikipedia.org/wiki/Irish_phonology
broad t's (next to broad vowels a o u) are dental, and
slender t's (next to slender vowels e i) are palatalized.
There are also on- and off-glides complicating the pronunciation of consonants.
The Wikipedia article is quite technical; there are more resources for pronunciation listed here: https://forum.duolingo.com/comment/30527560