The only criteria concerning the trade-in device they asked in preparing the quote are:
- Make
- Model
- Storage
- Carrier-designation
- Does the phone turn on
- Does the screen work properly and is free of cracks
- Can you factory reset the phone before shipping
If you are accurate in answering those, there should be no room for major diminution of the quoted price unless there is something else horribly off concerning the device's functionality, such as major functionality issues (cracks in the body / seams, volume buttons/headphone jack/speakers non-functional, etc).
If there's just a lot of wear such as 'finish' issues and light scratching on the display, you might expect something on the order of a 10-15% drop. A cracked rear glass on last year's Pixels might dock a bit, but shouldn't be too drastic as that's cosmetic.
The 3rd party doing this is going to look for anything they can to reduce what they have to pay, and it wouldn't surprise me if their reps reviewing the quotes are compensated for hitting a quota on how much they are able to reduce those offers... They're also going to figure most people would be more likely to accept a modest drop than to just take the phone back (which is in your rights).
Mine is showing as received by tracking (was in a sleeve, in bubble wrap, in a heavy duty shipping box), works perfectly, and would be almost indistinguishable from new (in case with screen protector from day 1) so I'm anticipating 100% of the offer extended to me. If it comes in lower, I'll just require them to ship it back to me and I'll sell it out on Swappa.