Hello, Heshel It's difficult to explain... It means that her operation is basically over. "or what's left of it" reffers to the part that is still active or 'not over', if I can say it like that. (It can also be a sarcastic way of saying that it was never going to last, and people suspected that that might be the case/ just that the operation is in fact over) I don't know how to paraphrase it either because it's a pretty bulky sentence... What's left of her operation was planned so it's participation would be visible and to show a desire to be helpful towards voter's concerns, and not to show support for the effort led by Green Party nominee Jill Stein. Basically, the effort was there to help voters and not to encourage them to vote for the Green Party. Hope this helps!!

What's left = the part which remains Hillary Clinton's campaign team does not want to clearly support the requests by the Green candidate for recounts. (This would look bad for Mrs Clinton.) Instead, it says that it will cooperate only in order to respond to voters' concerns.