Gayaru-chan doesn't want to be paid tribute, knowing her crush is gonna be spending it on her anyways.
People usually relate the "black market" expression as selling shady things, but it can also mean a sort of parallel market, outside of the formal, legal one where official transactions occur.
Think of people re-selling tickets for shows and events, that's not under the venue's jurisdiction and consumers have no means to shield themselves from abusive pricing or straight up being scammed, there are no rights and sellers don't have to be law-abiding, neither do buyers, so it is considered an underground/shadow economy. The key word is "informality" and lack of regulation is usually present. But it doesn't need to be selling guns, drugs or kidneys.
So in this example, the "legal market" is Haru's grandma (?) giving her the New Year's money, in the formal setting of "Relative gives money to someone from their family", and the "black market" Koyuki refers to is Haru trying to give her the money the same way people get something and try to resell it, be it for profit, be it because the source is not legit. Also giving her lunch money, New Year's money, any type of money intended to be for her makes it seem like she's Yuki's gofer or is being bullied, so it feels like giving the money is doing something wrong, the money being something that shouldn't be hers since the "legal" source doesn't necessarily consent with it being "sold" (given) but an informal agreement between them was made and now it is hers.
Black market is not necessarily the best way to describe it tho. The term grey market exists, but it's not common, as far as I know people just say black/underground market for things sold informally, like a dude coming up to you, opening his jacket and asking if you wanna buy [insert product here].
I tried to explain but I think I've spiraled. I'm an economist so I went 🤓☝️