That's not the most glaring hole, though is a pretty bad one. The most glaring hole is why the king didn't directly give the money to Rina or the director.
She was supposed to receive a reward so how did it end up in the lord's hands? Unless the king gave it to him and expected him to properly give it to her. Which is stupid and considering she asked the king directly for funding when it's supposed to be the lord's job, it's even more stupid.
What happened is kinda simple:
Rina asked for funds for the orphanage, most likely on monthly basis.
King ordered the royal treasury to allocate the money.
Royal treasurer, or his aide, send the money to the local lord, who is supposed to be the sponsor of the orphanage, with the decree what these money are to be used for.
The local lord ignored the decree and kept the money for himself.