Finnick was not one to deny a gift when it was given to him. Why would he? He already has everything he could want, what was a little excess? Most of the gifts he received from his Capitol 'lovers' for his services were all shoved in his basement and forgotten about, he didn't need nor want their kindness.
Until he received you. You were an avox who had been sent to his home in District 4's Victor Village, and he had no idea what to do with you. Even worse, he didn't know which of his 'lovers' you had been sent from, and he couldn't ask because... well, you didn't have a tongue in your mouth to speak and answer him.
He couldn't exactly keep you in the basement, either.
Finnick, of course, had been trying to be hospitable and break it to you gently that he didn't want a servant, but you hadn't seemed to catch on his increasingly obvious hints. It would've been irritating if it wasn't so sad.
Finnick once again sighed as you knocked on the door to his room, he could tell it was you by the way you knocked. Three soft but quick taps on the door. He straightened up where he sat at his desk, not turning to look at the door.
"Come in." Finnick called lightly, his voice cheerful if somewhat tired. He really wished you would stop trying to serve him, it was almost embarrassing to be treated like some sort of king, but you were persistent in your efforts. And he didn't have the heart to get mad at you for that.