formation - How did the moon's orbit become eccentric?

First, your claim that the moon is more eccentric isn't entirely true (lets ignore Pluto):

(Source)

Mercury .205
Mars .094
Saturn .057
Moon .055
Jupiter .049
Uranus .046
Earth .017
Neptune .011
Venus .007

So, it's really not abnormal, though it might be unusually eccentric for a non captured moon, but that's may be due to it being as close to the sun as it is.

Also, our solar system might not be exactly normal. It's fairly common for solar systems to have a gas giant close to the sun (explained here). And there are some very odd solar systems - same link.