I'm trying to make sure this is not on a mistake on my part, but when you decline the gift box, does that close it off altogether or allow you to retrieve it on another character?
I don't recall seeing a notification on my screen for the box today. I had was on one character online past the midnight reset, but when I re-logged I didn't get a prompt.
If you pressed the "Delete" button on the Reward Window instead of "Accept", unfortunately that means you won't be able to get the gift box anymore because you deleted it from your Reward Window.
I had this happened to me once on a different Hot Day gift when I selected "Delete". Or was it "Decline" back then, I don't remember...because this current Hot Day has "Accept" and "Delete" buttons. Either way, pressing "Decline" or "Delete" would remove the gift from the Reward Window.
If you didn't want to get the gift box on a particular character that you logged into, you can just press the "ESC" button or just close the window (by pressing X on the top right) to get rid of the Reward Window. Then, you would be able to claim the gift on another character.