Minor damage to car
 

So I did a weekly rental and am returning it today, and yesterday I had noticed that there is a rather large scratch on the top of the trunk. It's not deep, but is quite long. It looks like someone must have put luggage or a box on it and pulled it along.

I'm almost positive I didn't see it when I picked it up because unless you look at the right angle you can't see it too well. It is certainly there though.

Given that it's only a surface scratch (only the clear coat) if they do happen to notice it when I return it, does anyone know how much they might charge for minor scratches?

You haven't said where the rental is.
In Europe, I would expect that to be chargeable, but damage control in the US seems much more relaxed.

In my experience in the US, I've only had 2 notable damages to vehicles:

1. 4Runner where the antenna (front right quarter panel) was ripped off (left a jagged golf ball size hole in the panel). The quarter panel & hood had clear coat damage. The passenger door had paint damage. (Long story on how it happened....). The damages were approximately:
-$800 for antenna, paint/body repair (paid by Amex)
-Admin Fee (not paid by Amex)
-2 days loss of use (Not paid by Amex as I had screen shots showing vehicles available for the 2-weeks upon me turning in the vehicle)

I was in disbelief that it was so cheap to have the repair done. I was expecting a bill around $3000 or so for how bad it looked.

2. Had an Expedition XL that took a rock to the windshield from the construction truck in front of me. When I swapped it out, I filled out the accident paperwork & the agent said it "might be repairable, but most likely will be replaced." Never got a bill! (it's been 4 months by now)

Keep your fingers crossed! It took me 5 months to hear back from Avis after totaling a Malibu with 400 miles on it.

What you describe doesn't sound remotely like a "minor scratch." Bet you that they will want to, at a minimum, repaint the area.

Depending on how you are insured, there may be a requirement that you report the damage within a very limited period of time. If you miss that, you are on your own. So, check that and document the damage.