If you haven't watched season 3 yet, this is a SPOILER scene from 3.02 The Box.
Unpleasant Business
Too bad he's not blind. Wait. Is he actually suggesting we kill this guy?
Olivia Dunham was no more an assassin in this world than in her own world. The look on her face told Newton everything. He thought he was doing her a favour. Killing in cold blood after all was unpleasant business.
"If you need me to take care of him..."
"No, you can just do your job. Make sure you don't screw it up this time."
Olivia looked back at the man sitting in the kitchen again.
Sigh.
She was regretting what she had to do already.
She retrieved the silencer from the drawer and screwed it to the muzzle of her gun.
It's for your own good you know.
Sigh.
I'll make sure you won't feel any pain.
"I'm sorry." Too bad he couldn't hear her.
She kept her eyes opened when she pulled the trigger so she wouldn't miss.
I distinctly heard Olivia sigh twice when she was left alone with Joe before she killed him.
This is my interpretation for what went on in her mind at the time.