My sister and I noticed a white line (upper 3 mm of the paper or something) on the Rollercoaster Tycoon gift from Santa back when we still believed.. a few years later we found out that was because my father and brother had printed it themselves. The game was a copy. We thought it was funny.

I guess in the end it depends on the condition of what you're giving. And I don't think I'd do second-hand electronics.
And not everything has to be in perfect condition - depends on the item. Weathered wood has character, weathered plastic looks careless and ugly.

Can you try to teach your daughter the value of money? If she wants a new bike, say: OK, a second hand bike costs $100 and a new bike $500. You generally get a new bike every two years.. so you can have a new one in 8 years, or we can find a really pretty second-hand one now.
(Just realized the bike I got last year (I am 20) was my first ever new bike).
Buying everything new for a young kid.. well, how long will they actually use it? Bikes are outgrown fast, clothes too.
My parents aren't penny-pincers at all, neither are they poor. They just didn't see much use for spending a lot of money on a bike that would be outgrown within 2 years. (I still don't see the use of a new regular bike. I have an e-bike now, slightly different situation) I had new clothes and clothes that my sister had outgrown.

Just thinking- is it possible your kid is ashamed, afraid of being teased or bullied? Being thought of as poor? Maybe there's one or a few rich kids in her class and she wants to be like them because they are popular?