I have a translation of the 4th book by A-ba-ba-ha-la-ma-ha, a highly respected publishing house in Ukraine.
— То це ти син Артура Візлі? — спитав Муді. — Твій батько пару днів тому витяг мене з великої халепи… Так, я пробуду тут тільки рік. І то лише заради Дамблдора... один рік, а потім знову на пенсію.
"Special favor to Dumbledore...." was translated into "І то лише заради Дамблдорa..." which in Ukrainian unambiguously means "only for Dumbledore's sake".
Though, it really doesn't matter. Don't forget that it was said by Bartemius Crouch Junior who was disguised as Moody. I don't know the real reason* why Moody was invited to Hogwarts as a teacher** and I am afraid the author didn't mention it anywhere.
Nevertheless, "Special favor to Dumbledore...." is a clever reply. It lulls the pupils into thinking that Dumbledore and Moody are good old friends, and consequently raises fewer questions about Moody's past and why he is a teacher.
* The real reason why Dumbledore invited Moody to the school is the Triwizard Tournament.
** The position is vacant. I guess having an auror as a teacher is less suspicious than hiring an auror for security purposes.