Retired Runner getting back into play

[BeeCee]

Runner on third, 1 out.  Ball is popped up to shallow right field.  Runner does not wait for the catch and just runs home.  Right fielder does not make the catch but when the runner realizes they should have waited to possibly tag up they have already touched the plate.  They turn around and start running back to third thinking the RF made the catch.  The RF sees the runner  going back to third and throws the ball, overthrowing third.  Batter eventually gets to third on the overthrow.  There is an exception to the Interference rule that says just continuing to run the bases for a retired runner does not constitute interference.  However, was this continuing to run?  There is no call for a score so I don't think you can blame the RF for attempting the play unlike when a runner is called out.  Interference or no?  

[VolUmp]

NO.

The run scores. R3 didn't intentionally continue to run the bases for the purpose of confusing the defense. This happens all the time with runners retreating between bases because they thought the batted ball was caught only to see the trailing runner running right at them 

Once he scored, he can't "unscore."

[Rich Ives]

What VolUmp said.

[BeeCee]

Thank you for your reply.  I wasn't questioning if they score.  I guess I was more concerned about Could it be called interference? Being a retired runner got back in the play and influenced the throw could the batter\runner be called out for the player that scored running back into the play.  The RF doesn't know they touched home.  Really the R3 made the mistake and caused The R1 to get to 3rd by confusing the play.  

[VolUmp]

Understood your question. 

Answer: NO INT. 

Reasonable confusion that happens in the game.