When the CIA raided Yang Yi, he was gravely injured and nearly died, so naturally, he didn't have the chance to call Danny, and by the time he escaped from MI5, the situation had stabilized, so there still wasn't any need to call.
But after Kate was taken to Tang Guo's house, because the incident happened so close to Tang Guo's place, the panicked Kate did make a call to Danny.
Danny didn't say much to Kate, just a few brief words before hanging up, and his response had really pissed Kate off. She thought Danny was unwilling to lend a hand.
So, Kate never mentioned to Yang Yi that she had sought help from Danny, and she was still holding a grudge against him.
As a result, it was Tang Jianguo who told Yang Yi about the role Danny had played in this matter when they met.