Nevertheless, eight minutes for the settling of two suitcases and a hatbox is a long time. (2)
This isn't necessarily a quote about "innocence"—but it is a quote about shyness or naivety or a general inability to deal with something, which are all related to innocence in a negative way. The husband is clearly avoiding interacting with his wife and facing their issues—indicates some immaturity on his part. "Immaturity" actually might be a more accurate way of describing this theme than "innocence."
She looked as new as a peeled egg. (3)
Parker's description of the wife emphasizes her immaturity and innocence. An egg is, by definition, embryonic. It's pure and unsullied, but also is a far cry from a sentient being.
She had been staring raptly out of the window, drinking in the big weathered signboards that extolled the phenomena of codfish without bones and screens no rust could corrupt. (4)
You can take this sentence as describing symbols of innocence or an artificial sort of purity. A screen that doesn't rust or a codfish without bones might be convenient in some way, but they sort of go against the natural order of things.
"Ah, baby. Baby lamb. We're not going to have any bad starts." (112)
The husband (somewhat condescendingly) refers to the wife as a "baby lamb"—a lamb is traditionally a symbol of innocence, youthfulness, vulnerability, etc. But there's a certain irony in his statement that they won't have any bad starts—since they're sort of already having a bad start. But we bet he's thinking mainly about the sexytimes ahead.