Frank didn't force Bartlett at all, but his "kindness," the information he inadvertently revealed, and his nonsensical "suggestion" made Bartlett feel an inexplicable sense of "apology."
The feeling was complicated, a bit of guilt for Mervyn's death, gratitude for Frank's trust and letting him, a stranger, stay, and a mix of self-satisfaction and amusement at Frank's intention to marry him to his daughter (though it felt more like a farce).
Frank didn't fully use Mervyn's death and "shelter" to make Bartlett feel obligated to repay him, as that would make the request all the more blunt and transactional, or even coercive. Instead, he used a ludicrous reason to wrap up those matters, making his request easier for Bartlett to accept.
In short, all these factors together made it impossible for Bartlett to refuse.
"What's the matter?" He tried to put on an "angry" expression, but in his heart, he was already prepared to handle the matter.
