There's a good question, why did the U.S. ask India to send Khobragade out of the country. It was not an expulsion in the normal sense. There was a violation by India of its duty to the U.S. under U.N. rules. The answer, I guess, is that this is the minimum the U.S. could do and the State Dept. wants to reduce tensions.
If Khobragade really tries to carry out her threat to nonetheless remain in the U.S., the State Dept. would have to think of something else. I'll believe she's departed not when somebody says so, but when it's confirmed she's left U.S. soil - is there any evidence she has?