Michael and Roth said a lot of sweet nothings! and flattering each other, in Roth's house

Michael told Roth “I'll visit him [Pentangeli] soon
Why would Don Michael visit his “subordinate who, supposedly, was responsible for the Tahoe shooting?”
Pentangeli is a dead man “subordinate“ who tried to have his Don killed

My take, Michael's "Frank Pentangeli is a dead man--you don't object?" to Roth was more of a statement than question [ie: Michael was not “asking” for “Roth's permission”] in keeping with the continuation of their charade

Michael: "I want you to know about it [there is gonna be more blood shed] before it happens so that there's no danger of starting another war"
Roth: "Nobody wants another war"

I doubt even if Roth was “alarmed” that Michael “instead of having Frankie killed, he instructs him to have the meeting with the Rosato brothers” which “signalled” Michael “didn't suspect Frankie in the shooting after all--meaning that he must be suspecting someone else” [not Roth!] it would have mattered or bothered Roth because according to Roth, Michael was not coming back alive from Havana

I believe, Roth was not fooled by Michael's sweet nothings! either