There's never been any direct connection between Earth-3 Owlman (Thomas Wayne Jr., Bruce's older brother) and the Court of Owls. Remember, the Court of Owls had a different history
In the process, [Dick Grayson] discovered that the Court was actually merely the local branch of an international cabal of rich people, the Parliament of Owls.
The Parliament of Owls in and of itself was founded by people descended from the Tribe of Judas, who worshipped the Bat God Barbatos. Its true mission was to infect the blood of a son of the House of Wayne who had been prophesied to take on the persona of a bat, with five metals originating in the Dark Multiverse. The group had been promised that in doing so, they would be allowed to rule the world alongside Barbatos.
And we look at Barbatos to find that
Many centuries in the future, Barbatos' followers started to secretly prepare Batman to become the doorway for Barbatos to enter Prime Earth from the Dark Multiverse. His agents, by now known as the Court of Owls, planned to infect his body with each of the five heavy metals from the Dark Multiverse.
So there's not a direct connection that way. Barbatos has never been shown to have any interest in Owlman (hence why Thomas Wayne was Owlman and not Batman).
That should be the end of the story, right? Problem is, there is a direct connection between Earth-1's Lincoln March and the Court of Owls
"Lincoln March" is the alias used by a mayoral candidate in Gotham City who believes himself to be the younger brother of Bruce Wayne, Thomas Wayne, Jr.
It's never made clear if he actually is Thomas Wayne, or merely someone convinced he is. But, just like Earth-3's Thomas, he assumes an owl identity, but mainly to serve the purposes of the Court of Owls (which he winds up in charge of for a time)
Originally, March was a puppet for the Court [of Owls], meant to distract Bruce Wayne long enough for their Talon to easily kill him.
His Talon suit looks very owlish, given the source
Which raises the possibility that there is some yet-to-be revealed connection with the sources of the two Owlmen. The New 52 "reboot" never talks about any potential sources of Thomas Wayne's desire to take over Earth-3 and DC loves to make their multiverse characters similar in that regard.