The free shop gave me a giftbox with something inside, but when I go to the item page and click Open Box, it tells me there is an error.

What should I do?

I'd delete it. If you got it before the downtime, it's probably cause of that glitch.

I'm afraid I can't delete it :(

The only option is "Open Box"

I'd suggest filing a ticket if you can't delete it yourself...that's what the people who accidently put free-shop crystals in the crystal bank (they can't be removed) are doing.