This answer to the question What does the superiority of bani-israel (Children of Israel) over all beings mean? answers some aspects of the question above. But still I would like to answer the following in detail.
O Children of Israel! Remember My (Allah's) favour wherewith I favoured you and how I preferred you to (all) creatures. (Qur'an 2:122)
So, the children of Israel and Allah know better what was the favour being discussed above.
But, we can guess. Many places in Qur'an Allah was talking about the following keywords "children of israel", "favour", "covenant", "broke the covenant"... So, we can find that there is some link among each other.
First, of all, the main favour of Allah upon them(although not specifically mentioned) is the gifting of Torah and Injeel(Gospels given to Jesus(pbuh)). And then about the covenant.
O Children of Israel! call to mind the (special) favour which I bestowed upon you, and fulfil your covenant with Me as I fulfil My Covenant with you, and fear none but Me. (Qur'an 2:40)
And the verses Qur'an 2:63 and 2:83 talk further about the covenant. So to conlude this part, ask specifically to the Children of Israel(concerning the above keywords discussed), what all favours God made to them. But before you ask, a small reminder.
And if you should count the favors of Allah , you could not enumerate them. Indeed, Allah is Forgiving and Merciful. (Qur'an 16:18)
..different from the prophets he sent to the rest of mankind that we don't know the names of?
Allah sent messengers to every nation thereby favoring upon his grace to every nation by sending those prophets that we don't know the names of. But, just because they're not made examples set for us in the scriptures doesn't imply the favor made by Allah to them is either less or more.
why would Muhammad (peace be upon him) not be sent to the people Allah had already given so much to given the importance of Muhammad above all prophets?
The creator had his own reasons so as where to send Prophet Muhammad(pbuh). One simple reason is that God had to favor the Arab nation too as he favored the Children of Israel. (Qur'an 3:164)
Here the Christian claims that Israel was specifically chosen and prepared for the saving work which could then after Jesus be spread to the rest of mankind who never received the call to God. What is Islamic response to this?
I'm sorry, but there are verses which show Prophet Jesus(pbuh) of Nazareth was sent specifically(or only) to the lost sheep among the children of Israel. And he in turn commanded his disciples to do the same.
Go rather to the lost sheep of Israel. (Mat 10:6)
(Although I cherry picked no where did Jesus(pbuh) said go to the whole world).
May the creator guide us all.