It seems like Ted King's character Jack Finnegan (Finn's adoptive father) might be the biological father as well as being the adoptive father. They are showing him talking to himself in his mind (but not aloud) trying to figure out whether he should say something. And he was very concerned today when Steffy and Finn decided to post online or text or email the wedding invitations for anyone to see - he clearly didn't want someone to happen to see it.
edit to add:
If Jack is not the biological father, he knows something, or someone, connected to Sheila. The spoiler for later this week is that someone is concerned when a mystery woman arrives. Presumably that's about him and Sheila?