He didn’t even try the weak pretence of “present company excepted”. Wizard’s have terrible social skills, it’s not just Harry.
Eb hadn’t ever met Harry other than in his capacity of his Master/mentor, nothing really to hide, and that is Eb’s fault due to his theory of childraising. They had no other connection. Bad Eb.
He really only started his grandfatherly relationship with Harry after the soulgaze, probably when he realised he wouldn’t have to execute him.
I suspect during Next Book the existence of Maggie becomes widely known amongst the Supernatural community, and Harry basically says:-
“Come for me, not my daughter if you have a beef with me.”
“The Red Court went for my daughter, kidnapped and brutalised her. I rendered them extinct. All of them.”
“Nicodemus Archelone threatened my daughter, I gave him the very worst day in his very long life, and I haven’t finished with him yet and I WILL kill him, because I can.”
“The Titan tried to kill my daughter. Ask her how that worked out. If you can find her. Please try to find her.”
“Mortal or immortal, threaten my daughter and it’s the last thing you will ever do.”
His views on the subject are diametrically opposed to Eb’s, so no wonder it didn’t come out in the soulgaze.