I’m usually against using the word “that” — it’s often nothing more than a bit of shredded cardboard, completely worthless and utterly expendable.
Here, I think it’s necessary — because Mueller has people.
So by the end of the first line, I might think this is about Flynn saying something to the Mueller people.
In fact, I can still labor under this misimpression well into the second line: It seems Flynn said something to the Mueller people who are connected to the Trump administration or Congress.
Uh, no. When I finally get to the third line, and the verb “attempted,” my train goes off the tracks.
A simple “that” would have spared me the wreck: “Michael Flynn told Mueller that people connected to Trump admin or Congress attempted to influence him.”
It could have been worse, of course: “Flynn people told Mueller people connected to Trump people or Congresspeople…”