From the article:
"Specifically, the Court’s own conduct, coupled with the Principal Law Clerk’s* unprecedented role in the trial and extensive, public partisan activities, would cause even a casual observer to question the Court’s partiality," they write.
(Note that I believe it is unethical to spread the Principal Law Clerk's name around, and so I removed it from that quote.)
The Principal Law Clerk is exactly performing her role as it exists in New York. Judge Engoron seems to prefer paper notes over electronic messages, which is the only reason why Trump's team can even detect this interaction. If Judge Engoron were more technologically hip, he'd be communicating with her using instant messages.
But this is exactly what her role is. She is doing exactly what NY law says she should be doing. If the Judge asks his Law Clerk to point out when testimony conflicts with earlier testimony, for example, then it is incumbent upon her to pass him a note when she detects it. This is a big case, and there is a lot of information. She is there to assist Judge Engoron.
I am confident that Trump's legal team is not so stupid that they don't understand this. This motion has no chance to succeed.
What is actually happening is that Judge Engoron has gagged Trump from attacking his staff, but Trump is finding another way to attack them. He's hoping that some harm will come to her, and that this will stop people from prosecuting him.