The refusal is total and the reason is explicit: Abram will not allow the king of Sodom to be able to claim credit for his wealth. The phrase 'a thread to a shoelatchet' is a Hebrew idiom for the smallest possible thing. Abram's integrity is absolute — he will not let any worldly king take credit for what God has done.
Memory phrase: Don't let the wrong person take credit for what God has done.
Talk about it: Abram refused everything so that nobody could say they made him rich. Why does it matter who gets the credit for what we have?
Prayer: God, let all that I have come from You — and let everyone see that it does. Don't let me trade Your blessing for the world's reward.