White towel?

Because the private jet was commandeered/leased from a rich Libyan oil executive to firstly fly in a small element of CIA and JSOC Operators like the Delta boys and Fmr SEAL Glen Doherty from the US Embassy in Tripoli to Benghazi as a small Quick Reaction Force.

The pilots and stewardesses were employees of and paid by the rich Libyan oil executive and they didn't want to have the whole PRIVATE jet full of blood from wounded CIA/GRS personnel especially Mark "Oz" Geist who had the bottom of one arm flapping around barely holding on by the skin and had blood everywhere.

So to answer your question even though the CIA/State Dept leased the plane the stewardesses were still responsible for keeping the expensive jet clean and keep their jobs! You could see the reactions on their faces like when one woman stewardess puts her hand up to her mouth in shock at the state of how badly wounded some personnel were!
The leased private jet then flew back to the capital Tripoli and given back to its owner. Then at 7pm local time the Americans were transported out of Tripoli on a C-17 military aircraft, heading for Ramstein Air Base, Germany.

If you are not willing to give up everything, you have already lost