I was folding laundry in the dark and watching Judge Judy rip this guy a new asshole when the doorbell rang. This is very crass. Personally I would avoid using the word "asshole" until I had established the voice of the narrator, so it doesn't feel like a slap in the face. I don't know, maybe that's what you were going for. Also, this sentence is very complex without any use of commas to organize it, and could benefit from reorganization.
I flipped down a pair of Oakley wrap-around sunglasses and, still holding a pair of little Anthony’s cotton briefs in one hand, opened the front door. "Flipped down" doesn't mean anything to me, or if it does it means flipped them onto the ground. But after reading further, I find you mean "flipped a pair of Oakley wrap-around sunglasses down over my eyes." Which is not the most concise way of saying it, but it's more clear. "a pair of little Anthony's cotton briefs" is a lot of description for one pair of underwear. Try to be more concise while still capturing the picture, for example, "my child's cotton briefs." I would also use a long dash to interrupt the sentence instead of a comma here, since a comma after "and" and not before at first appears to be a mistake.
The light, still painfully bright, poured in from outside. I squinted behind my shades and could just made out the image of a UPS deliveryman.
And, oh, what an image it was.
As my eyes adjusted to the light, a hunky guy with tan legs and beefy arms materialized through the screen door before me. He grinned at me easily, showing off a perfect row of white teeth. Spiky yellow hair protruded from under his brown cap. The guy should have been a model, or at least my new best friend. "materialized through the screen door" makes it seem like he's moving through the screen like a ghost. Also, there wasn't a screen door there when we looked out the door a few paragraphs ago. Perhaps say "poured in through the screen door" there, and "materialized before me" here. Also, is his hair actually yellow (ew), or is it blond? This guy sounds like he's supposed to be perfect, but it comes off like a fake Ken doll, which makes me instantly dislike him.
“Mrs. Moon?” he asked. His eyes seemed particularly searching and hungry, and I wondered if I had stepped onto the set of a porno movie. Interestingly, a sort of warning bell sounded in my head. Warning bells are tricky to discern, and I automatically assumed this one was telling me to stay away from Mr. Beefy, or risk damaging my already rocky marriage. "His eyes seemed particularly searching and hungry" as in most people have searching, hungry eyes, but these are more so? Lose "particularly." Why is it interesting that warning bells sounded? It seems perfectly reasonable given this situation.
“You got her,” I said easily, ignoring the warning bells.
“I’ve got a package here for you.”
“You don’t say.”
“I’ll need for you to sign the delivery log.” He held up an electronic gizmo-thingy that must have been the aforementioned delivery log. Entirely unnecessary.
“I’m sure you do,” I said, and opened the screen door and stuck a hand out. He looked at my very pale hand, paused, and then placed the electronic thing-a-majig in it. As I signed it, using a plastic-tipped pen, my signature appeared in the display box as an arthritic mess. The deliveryman watched me intently through the screen door. I don’t like to be watched intently. In fact, I prefer to be ignored and forgotten. "and opened the screen door and stuck a hand out" there are better ways to word this. The sentence beginning "As I signed it" could also benefit from rewording and shortening. Here's where I hit a big stumbling block: your character flirted readily enough, but now says she prefers to be forgotten. If that were the case she would have been more reserved. It doesn't fit at all with the previous voice.
“Do you always wear sunglasses indoors?” he asked casually, but I sensed his hidden question: And what sort of freak are you?
“Only during the day. I find them redundant at night.” I opened the screen door again and exchanged the log doohickey for a small square package. “Thank you,” I said. “Have a good day.”
He nodded and left, and I watched his cute little buns for a moment longer, and then shut the solid oak door completely. Sweet darkness returned to my home. I pulled up the sunglasses and sat down in a particularly worn dining room chair. Again, "pulled up" makes no sense here, use "pushed my sunglasses to the top of my head" or just have her take them off.
Overall thoughts: Meh. You have a lot of wording issues that need to be more clear and concise, your voice seemed formed and then was broken entirely with a switch to an introverted thought, and I don't understand why a Ken-doll perfect guy would be a delivery man instead of in LA trying to be an actor, or being something else that takes advantage of his looks, at least a waiter. Delivery drivers don't take care of themselves. I haven't read the book, so it's totally possible that this guy shows up again and he was really a spy who was out to locate Mrs. Moon so he could take her down, in which case he would have tried to look like a delivery driver more instead of a body-builder/porno star.
What do you think? Anything to add, or that you disagree with? Have a great Tuesday!