I think Liz just might as well of told Stella---the whole point of bringing you and Laura back was to get you fired at the first chance I got. But, that plan backfired and you're still here.
So, from getting into the taxi and then at the house, she's now trying to undermine Stella psychologically. I think Liz just showed she's frightened of Stella while Laura wasn't a real threat to her.
I think last week with the chips, Stuart volunteering Stella as PM was his attempt to get rid of her too and on this task was trying to put himself into a win-win situation no matter the outcome. Liz is somewhat not as subtle with her attempt after it failed.